MODULE 8
FROM THE UNIVERSE TO THE ATOM
Table of contents for Module 8 - From the Universe to the Atom
Introduction to From the Universe to the Atom............................................................................................................1
Origins of the Elements...................................................................................................................................................2
Question sheet 8.1 ............................................................................................................................................... 9
Simulation stellar nucleosynthesis ....................................................................................................................... 13
Question sheet 8.2 ............................................................................................................................................. 16
The origin of spectra .............................................................................................................................................. 17
Question sheet 8.3 ............................................................................................................................................. 27
Structure of the atom ..................................................................................................................................................... 30
The electron ............................................................................................................................................................ 32
Th m n cha ge-to-mass experiment ................................................................................................................. 36
Question sheet 8.4 ............................................................................................................................................. 39
Millikan il d e e imen ................................................................................................................................... 41
The nuclear model of the atom ............................................................................................................................ 43
Rutherford's atomic model .................................................................................................................................... 45
Chad ick di c e f he ne n....................................................................................................................... 45
Conservation of kinetic energy and momentum ................................................................................................ 47
Properties of neutrons ........................................................................................................................................... 48
Question sheet 8.5 ............................................................................................................................................. 48
Quantum Mechanical Nature of the Atom .................................................................................................................. 50
Question sheet 8.6 ............................................................................................................................................. 54
Question sheet 8.7 ............................................................................................................................................. 57
Question sheet 8.8 ............................................................................................................................................. 61
Properties of the Nucleus ............................................................................................................................................. 64
The spontaneous decay of unstable nuclei ........................................................................................................ 65
Question sheet 8.9 ............................................................................................................................................. 70
Question sheet 8.10........................................................................................................................................... 79
Question sheet 8.11........................................................................................................................................... 89
Deep inside the atom..................................................................................................................................................... 91
Question sheet 8.12........................................................................................................................................... 99
From the Universe to the Atom - revision questions ................................................................................... 103
Learning Across the Curriculum Icons
You will notice that the syllabus and these study guides have some strange looking icons throughout. These are described
as Learning Across the Curriculum Icons and give students and teachers some additional guidance on cross-curriculum
priorities, general capabilities and other areas identified as important learning for all students. The icons are as follows:
Cross-curriculum priorities
Aboriginal and Torres Strait Islander histories and cultures
Asia and Australia s engagement with Asia
Sustainability
General capabilities
Critical and creative thinking
Ethical understanding
Information and communication technology capability
Intercultural understanding
Literacy
Numeracy
Personal and social capability
Other learning across the curriculum areas
Civics and citizenship
Difference and diversity
Work and enterprise
NSW Physics Stage 6 syllabus © NSW Education Standards Authority for and on behalf of the Crown in right of the State of New South Wales, 2017.
From the Universe to the Atom glossary
Absolute The absolute magnitude of a celestial object, such as a star, is the brightness
magnitude measured by an observer at a distance of 10 parsecs from the object. The smaller
the number, the greater the brightness.
absorption
spectrum A spectrum in which there is a decrease in intensity of radiation at specific
wavelengths depending on the absorbing substance. This is observed as a pattern
alpha radiation of dark lines crossing a continuous spectrum.
artificial nuclear
transmutation A helium nucleus emitted from a radioactive nucleus.
atomic mass unit u
The changing of a nucleus artificially. An example is when nitrogen is
Balmer series bombarded with alpha particles to produce oxygen and hydrogen.
beta radiation One atomic mass unit is defined as exactly 1/12 the mass of an atom of carbon-
Big Bang 12.
nucleosynthesis
The series of spectral emission lines from the hydrogen atom due to electron
Big Bang theory movements from higher levels down to the second energy level. Four transitions
occur in the visible region giving four coloured lines.
binding energy
An electron emitted from the nucleus of a radioactive atom.
Bohr atomic model
The production of nuclei shortly after the Big Bang, that is the formation of
CMBR hydrogen (H-1), its isotope deuterium (H-2), the helium isotopes He-3 and He-
4, and the lithium isotope (Li-7).
CNO cycle
The widely accepted theory about how the universe began. It says that the
continuous universe started with a small singularity that inflated over the next 13.8 billion
spectrum years to what we now observe.
de B glie ma e
waves The energy that holds a nucleus together. It is found from the relationship
E = mc2 where m is the mass defect of the nucleus and E the binding energy.
galaxy
The first model to use quantum theory. It states that atoms absorb or emit
gamma radiation radiation only when electrons jump between allowed, or stationary, states.
half-life
Hertzsprung Shorthand for cosmic microwave background radiation which is leftover
Russell diagram radiation from the Big Bang.
Hubble-Lemaitre
law The Carbon-Nitrogen-Oxygen cycle is the main source of energy in larger main
sequence stars which fuse hydrogen into helium so that four hydrogen nuclei are
light year changed into one helium nuclei.
luminosity
A spectrum having all wavelengths present. It is usually produced by hot solids,
main sequence for example, a tungsten filament light globe.
stage
A hypothetical wave related to the motion of a particle of atomic or subatomic
size which explains effects such as the diffraction of beams of electrons by
crystals.
A collection of stars, planets, gas, dust, and dark matter held together by gravity.
Our milky way galaxy is thought to contain somewhere between 100 to 400
billion stars.
High energy electromagnetic radiation emitted following beta or alpha decay.
The time taken for the radioactivity of an isotope to fall to half its original value.
A graph of the temperature of stars against their luminosity, or the colour of
stars, or spectral type, against their absolute magnitude.
This law states that the red shift in the spectra of distant galaxies (and hence their
speeds of recession) is proportional to their distance. It was until recently just
known as Hubble s law.
The distance that light travels in one year.
A measure of the amount of energy an object emits in a fixed time, often
measured in Watts. We can also compare to the luminosity of the sun, for
example a star may be written as being five times as luminous as the sun.
The main sequence is a continuous and distinctive band of stars that appears on
the Hertzsprung - Russell diagram. Most stars in the universe are main sequence
including the sun. Their energy source is the conversion of H to He, either by
the pp cycle or in larger mass stars by the CNO cycle.
mass defect The difference between the mass of a nucleus, and the sum of the masses of the
nucleons that make it up.
neutrino A subatomic particle very similar to an electron but with no electrical charge and
a very small mass which could be zero.
nuclear fission The splitting of a large atom into smaller nuclei so releasing energy.
nuclear fusion A reaction in which atomic nuclei of low atomic number fuse together to form a
heavier nucleus so releasing energy.
OBAFGKM The spectral sequence of main sequence stars, O B A F G K M. A common
mnemonic to remember this is Oh Be A Fine Girl (or Guy or Gorilla), Kiss Me.
parsec pc A unit of distance equal to about 3.26 light years (3.1 × 1016 metres).
positron A positive electron which is the antiparticle or antimatter counterpart of the
electron.
post main sequence The stage of life of a star after it has left the main sequence and is now burning
helium , that is converting helium into larger atoms, for example, carbon.
pp cycle The main source of energy in the sun and other cool main sequence stars where
four hydrogen nuclei are converted into one helium nuclei.
radioisotope A radioactive element, consisting of atoms with unstable nuclei, which undergo
radioactive decay to become more stable by emitting alpha, beta, or gamma
red giant stage radiation.
R he f d A dying star in the last stages of stellar evolution.
atomic model This model has electrons orbiting a small positively charged nucleus. The
nucleus contains protons only as the neutron had yet to be discovered when this
Schrödinger model was introduced.
A physicist who contributed to the model of the atom by using mathematical
singularity equations to describe the probability of finding an electron in a certain position.
A point in space-time where matter is infinitely dense and the laws of physics as
standard model of we know them stop working.
matter A theory of fundamental particles and how they interact.
stellar spectra
universe The spectra produce by stars. They are usually absorption spectra.
white dwarf All the mass and space that exist.
A star at the end of its life where there are no nuclear reactions.
A periodic table is essential for this module. You should download the periodic table from the NESA website
as this is what you will be provided with in the HSC examination.
Data sheet Planck constant, h = 6.626 x 10-34 Js
Charge on the electron, qe = - 1.602 x 10-19 C Rydberg constant, R (hydrogen) = 1.097 x 107 m-1
Mass of electron, me = 9.109 x 10-31 kg Atomic mass unit, u = 1.661 x 10-27 kg
Mass of neutron, mn = 1.675 x 10-27 kg
Mass of proton, mp = 1.673 x 10-27 kg = 931.5 MeV/c2
1 eV = 1.602 x 10-19 J
b = 2.89 x 10-3 m K
Formulae sheet
E = hf = ℎ 1 = 1 − 1
= ℎ 2 2
= − = 2
1/2
= 2 m =
Introduction to From the Universe to the Atom
Humans have always been fascinated with the finite or infinite state of the Universe and whether there ever
was a beginning to time. Where does all the matter that makes up the Universe come from? Ideas and
theories about the beginnings of the Universe, based on sound scientific evidence, have come and gone.
Current theories such as the Big Bang theory and claims of an expanding Universe are based on scientific
evidence available today through investigations that use modern technologies. Evidence gathered on the
nucleosynthesis reactions in stars allows scientists to understand how elements are made in the nuclear
furnace of stars. On scales as large as the Universe to those as small as an atom, humans look to the sky for
answers through astronomical observations of stars and galaxies.
Beginning in the late 19th and early 20th centuries, experimental discoveries revolutionised the accepted
understanding of the nature of matter on an atomic scale. Observations of the properties of matter and light
inspired the development of better models of matter, which in turn have been modified or abandoned in the
light of further experimental investigations.
By studying the development of the atomic models through the work of Thomson and Rutherford, who
established the nuclear model of the atom a positive nucleus surrounded by electrons students further
their understanding of the limitations of theories and models. The work of Bohr, de Broglie and, later,
Schrödinger demonstrated that the quantum mechanical nature of matter was a better way to understand
the structure of the atom. Experimental investigations of the nucleus have led to an understanding of
radioactive decay, the ability to extract energy from nuclear fission and fusion, and a deeper understanding
of the atomic model.
Particle accelerators have revealed that protons themselves are not fundamental and have continued to
provide evidence in support of the Standard Model of matter. In studying this module, students can
appreciate that the fundamental particle model is forever being updated and that our understanding of the
nature of matter remains incomplete.
Outcomes
A student:
analyses and evaluates primary and secondary data and information PH11/12-5
solves scientific problems using primary and secondary data, critical thinking skills and scientific
processes PH11/12-6
communicates scientific understanding using suitable language and terminology for a specific
audience or purpose PH11/12-7
explains and analyses the evidence supporting the relationship between astronomical events and the
nucleosynthesis of atoms and relates these to the development of the current model of the atom
PH12-15
NSW Physics Stage 6 syllabus © NSW Education Standards Authority for and on behalf of the Crown in right of the State of New South
Wales, 2017.
Module 8 From the Universe to the Atom 1
Origins of the Elements
Students:
investigate the processes that led to the transformation of radiation into matter that followed the
Big Bang
investigate the evidence that led to the discovery of the expansion of the Universe by Hubble
(ACSPH138)
analyse and apply Einstein s description of the equivalence of energy and mass and relate this to
the nuclear reactions that occur in stars (ACSPH031)
account for the production of emission and absorption spectra and compare these with a continuous
black body spectrum (ACSPH137)
investigate the key features of stellar spectra and describe how these are used to classify stars
investigate the Hertzsprung-Russell diagram and how it can be used to determine the following
about a star:
characteristics and evolutionary stage
surface temperature
colour
luminosity
investigate the types of nucleosynthesis reactions involved in Main Sequence and Post-Main
Sequence stars, including but not limited to:
proton proton chain
CNO (carbon-nitrogen-oxygen) cycle
NSW Physics Stage 6 syllabus © NSW Education Standards Authority for and on behalf of the Crown in right of the State of New South
Wales, 2017.
Inquiry question: What evidence is there for the origins of the elements?
With all inquiry questions consult with class members, come to a consensus and then summarise your answer in the
space provided.
2 Module 8 From the Universe to the Atom
The Big Bang
Astronomers hypothesise that billions of years ago the universe was no larger than the dot at the end of this
sentence. This tiny universe, described as a singularity, was extremely hot and dense. The universe then
expanded in what astronomers call the Big Bang. According to the Big Bang theory, the universe formed
in an instant, 13.8 billion years ago.
Evidence for the Big Bang
The evidence for the Big Bang has been researched for many years and includes:
the expansion of the universe
Cosmic Microwave Background Radiation (CMBR)
transformation of radiation into matter, that is the making of hydrogen and helium.
We now look at these points in detail.
Transformation of radiation into matter, that is the making of H and He
Evidence that supports the Big Bang is the production of hydrogen and helium. This is described as the Big
Bang nucleosynthesis, that is the making of the light elements, H and He. Stellar nucleosynthesis which
happened much later in stars is the formation of all the other elements.
In the 1950's and 60's, the main theory regarding the formation of chemical elements suggested that all
elements were produced either inside stars or during supernova explosions. This however led to a problem
with the amount of helium observed. The theory estimated if stellar nuclear reactions were the only source
of helium that there should only be about 1 - 4% present in the universe. This however did not agree with
the observation that more than 25% of the universe is helium.
This led to a modification of the Big Bang theory so that it started with a high density and very hot
temperature, that is a hot Big Bang. These starting conditions of the early Big Bang were suitable for
producing helium from fusion. Elements heavier than lithium are produced in the interiors of stars much
later in the universe's history whereas light elements such as deuterium, helium, and a very small percentage
of lithium were produced in the first few minutes of the Big Bang.
This is a common theme throughout science that when a theory no longer fit the experimental evidence then
the theory is either modified, as is the case here, or discarded.
In the first seconds of the universe's existence the temperature was billions of degrees, which was much too
hot for nuclei to join together. The universe was about the size of the sun, and can be thought of as a hot
collection of radiation and fundamental particles such as quarks which were produced as energy changed
into mass. Three minutes after the Big Bang, the temperature of the universe had cooled to approximately
one billion Kelvin which allowed nucleosynthesis, that is the production of the light elements, to occur.
Protons and neutrons collided to produce deuterium 12 , and then deuterium collided with other protons
and neutrons to produce helium and small amounts of tritium 31 . The following diagram shows one of the
reactions involved in the Big Bang nucleosynthesis.
proton forms forms P forms
deuterium tritium helium-4
P
PP P N
N N
NN P
N N
neutron
We can summarise this as follows: 2 11 + 2 01 → 42
Module 8 From the Universe to the Atom 3
About 98% of the helium present in the universe today was produced not in stars, but in the first few minutes
of the Big Bang. Within the next half hour, when lithium 7 was created, the universe cooled and expanded
to a point where fusion of heavier elements was impossible. Much greater densities and temperatures are
required if, for example, two helium nuclei are to collide and join. This is because the charge on each is
plus two and from Coulomb s law a force four times as large is required compared to that between two
hydrogen nuclei. Forces as large as this require extremely high temperatures and pressure such as that found
in the core of a star.
Summary
Nuclear physics predicts that a hot Big Bang will produce hydrogen, helium and a very small percentage
of lithium. When calculations are compared to that observed by astrophysicists, they are found to be almost
identical, hence giving support to the Big Bang theory.
Task
Watch the YouTube video searching for the term, Nucleosynthesis: The Formation of Elements in the
Universe . Open Concentrate on the first two and a half minutes of this video. Answer the following
questions:
What are the three main types of nucleosynthesis?
Three minutes after the big bang which nuclei were formed?
What was able to be formed 300000 years after the big bang?
Where does nearly all the hydrogen and helium that exist in the universe come from?
What is the ratio of hydrogen to helium in the universe?
What is the ratio of hydrogen to helium evidence of?
What is stellar nucleosynthesis?
Note: all the hydrogen in the universe was produced in the Big Bang.
4 Module 8 From the Universe to the Atom
Another important piece of evidence supporting the Big Bang is the expansion of the universe.
Module 8 From the Universe to the Atom 5
The expansion of the universe
The astronomer Hubble observed red shift in the spectra of many galaxies. The spectrum of the sun (top
diagram) and light from distant galaxies (bottom diagram) is shown below. You will observe that the dark
absorption lines have been shifted towards longer wavelengths, the red end of the spectrum, in the light
from distant galaxies hence the term red shift. We know from the Doppler equation, see module 3 - Waves
and Thermodynamics, that red shift, that is a longer wavelength, or shorter frequency, means that the object
is moving away from us.
460 500 550 600 650 700 wavelength (nm)
sun
distant galaxy
The shift in wavelength The shift in wavelength
Hubble discovered that most galaxies are moving away from us and away from each other. Hubble worked
out the relationship that the farther away a galaxy is, the faster it is moving away from us. This is given by
Hubble s law: v = Hd
where H = Hubble's constant
d = distance the galaxy is away from us
v = velocity of galaxy (proportional to the redshift)
Hubble s law
The graph below plots velocity against distance for various galaxies. This shows a direct relationship
between velocity and distance. The further away the galaxy, the greater the velocity. The gradient of the
graph is the Hubble constant, H.
v/104 km s 1
8
7
6
5
4
3
2
1
0
0 400 800 1200
d/Mpc
Note the distance is given in units of Mpc. A megaparsec (Mpc) is a million parsecs.
One pc is equal to 3.1 x 1016 m.
6 Module 8 From the Universe to the Atom
Astronomers interpret this graph as galaxies expanding away from each other except for those that are close
to us where gravitational attraction is significant. This suggest that there was a common starting point, that
is all the material started from a single point, a singularity. This provides strong support for the Big Bang
theory.
Hubble s Law which describes the way in which galaxies move away from each other and is fundamental
to the theory of the Big Bang was renamed in October 2018 by the International Astronomical Union as the
Hubble-Lemaître Law.
Task
Using the graph on the previous page draw a line of best fit and from this find Hubble s constant giving the
units in km s-1 Mpc-1.
As you can see from this graph the points do not lie on a perfect straight line, they have some variation.
One way to measure this variation is to draw a line of best fit and then a worst line of best fit. This can be
used to express your answer as an uncertainty in the Hubble constant, that is have a value of H ± H.
Watch the following YouTube video to see how this works. Search for A Level Practical Endorsement -
Percentage Uncertainty in a Gradient Open
Express your answer for Hubble s constant using this concept.
Research task
Find out who Georges Lemaître was and why his name is now linked to that of Hubble.
Module 8 From the Universe to the Atom 7
CMBR cosmic background radiation
Another piece of evidence that supports the Big Bang is cosmic background radiation, CMBR.
Search YouTube for Cosmic Microwave Background (CMB): Universe's First Light Open to answer the
following questions.
What is CMBR evidence of?
What is a photon baryon fluid and what is it made of?
Give two examples of baryons.
What happened about 380000 years after the Big Bang?
What has happened to the photons from the early cosmos?
What was the name of the two scientists who first discovered CMBR and how did they discover this? Note
you may have to do further research.
Sample problem 8.1
Describe how Hubble s observations of the redshifts of galaxies was used to develop Hubble s Law and
explain how Hubble s Law is used to support the Big Bang theory.
Solution:
Hubble observed that all moving galaxies have a Doppler shift in their spectrum. This shift he found was
proportional to the speed of the galaxy. Nearly all the galaxies that Hubble measured were redshifted which
means that they are moving away from us. The greater the redshift the faster the object is moving.
Hubble plotted redshift, that is velocity, against distance and obtained a straight-line graph. This is now
known as Hubble s Law which states that the more distant the object, the faster it is moving this means
that there was a common starting point, that is all the material in the universe came from a single point, a
singularity, which supports the Big Bang.
8 Module 8 From the Universe to the Atom
Question sheet 8.1
1. (a) Describe what is meant by cosmic background radiation (CMBR).
(b) Explain how cosmic background radiation is evidence which supports the Big Bang model.
(c) State two other pieces of evidence that support the Big Bang model.
(d) A student writes in an exam the following; a a e l of he Big Bang, he ni e e i e anding
into a ac m . Discuss whether the student is correct.
2. Light arriving at the Earth from a distant galaxy is observed to be red shifted.
(a) Explain, in terms of spectral lines, what red shift means.
(b) Explain how this red shift is in agreement with the movement of distant galaxies.
3. Describe evidence for the hot Big Bang model of the universe. ..
..
Module 8 From the Universe to the Atom ..
..
..
..
9
4. A galaxy is 5.2 × 1024 m from the Earth. Find the speed of this galaxy, in km s-1, relative to the Earth
given that:
Hubble s constant, H = 65 km s-1 Mpc-1 and 1 parsec (pc) = 3.1 × 1016 m.
5. It is believed that the universe is expanding with the galaxies receding from each other. The graph below
shows some of the experimental data which support Hubble s Law. Each point on the graph represents
a galaxy with v the recession speed of a galaxy and d its distance from Earth.
v/104 km s 1
8
0
0 400 800 1200
d/Mpc
(a) Draw a line of best fit and hence find the value of the Hubble constant H in units of km s 1 Mpc 1.
(b) A galaxy has a recession speed of 60000 km s-1. Calculate its distance from Earth in Mpc.
6. The age of the universe, T, can be calculated by the time it has taken for a galaxy, travelling at speed v,
to recede a distance d from ours. This gives: T= and as v = Hd then we get T = 1 .
Note with this equation to get T in seconds then H, the Hubble constant, has to be in SI units. Use this
equation to estimate the age of the universe in years. Take the value of H as 65 km s-1 Mpc-1 and one
year as 3.2 × 107 s. 1 pc = 3.1 x 1016 hence 1 Mpc = 3.1 x 1022 m.
10 Module 8 From the Universe to the Atom
Einstein s equivalence of energy and mass equation
As we saw in module 7, the nature of light, energy is related to mass by the formula E = mc²
where E = energy in Joules, m = mass in kg and c the speed of light.
This relationship means that mass can be converted into energy and the reverse is also true; energy can be
converted into mass. This is what happened in the Big Bang when energy in the form of radiation was
converted into mass.
Atomic masses are usually given in atomic mass units (u)
1 u = 1 mass of a carbon 12 atom (by definition) = 1.661 x 10-27 kg
12
The energy equivalent to 1 u can be found from E = mc² = 1.661 x 10-27 x (3 x 108)2 = 1.49 x 10-10 J
and converting to electron volts we divide by the charge on an electron 1.602 x 10-19 C.
This gives E = 1.49 x 10-10 1.602 x 10-19 eV = 931.5 x 106 eV or 931.5 MeV
Therefore 1 u has 931.5 MeV of energy. As m = 2 then we see this mass written as 931.5 MeV/c2 in the
data sheet.
An alternative symbol for atomic mass unit which you may come across instead of u is amu or dalton, Da.
Representing nuclei
We represent the nucleus of an element as follows: X
where A is the mass number which is the number of protons and neutrons
Z is the atomic number which is the number of protons
X is the symbol for the element.
The atomic number tells you which element is present. If Z = 6 this means that X is carbon (C).
The mass number is always a whole number and is equal to the number of protons plus neutrons.
Nucleon is the general term used for both protons and neutrons.
Isotopes are atoms having the same atomic number Z but different mass number A. For example, 12 C
6
and 14 C are isotopes of carbon. 12 C is referred to as a carbon 12 isotope.
6 6
A radioactive atom, an atom which emits radiation, is called a radio-isotope.
The atomic mass of an atom is the mass compared with the mass of the carbon-12 ( 12 C ) isotope. A 12 C
6 6
atom is defined as having a mass of exactly 12 atomic mass units (u). The atomic mass is nearly always
not a whole number.
The following table shows the properties of the nucleons and electrons.
particle charge (C) mass (kg)
proton + 1.602 x 10-19 1.673 x 10-27
neutron 1.675 x 10-27
electron 0 9.109 x 10-31
- 1.602 x 10-19
Task:
Working in pairs quiz each other on the definitions given above.
Module 8 From the Universe to the Atom 11
The nuclear reactions that occur in stars
As we shall see later in this module when we study what are called HR diagrams, stars fall into different
categories. The stage where a star spends most of its lifetime is called the main sequence. A star in this
stage converts hydrogen to helium in its core. The mass of four hydrogen nuclei 1 H is greater than the
1
mass of one helium nuclei 4 He . This difference in mass is converted into energy by Einstein s equation,
2
E = mc2, and this provides the energy to power the star. This energy is mainly released as electromagnetic
radiation, that is visible light, IR, UV, radio and gamma rays from the surface of the star.
Nuclear reactions in main sequence stars
The proton-proton chain (PP cycle)
The proton-proton (PP) chain is the main type of nuclear reaction in lower mass, cooler main sequence
stars, for example, our sun. In the core of a star like the sun the temperature is high enough (15 x 106 K) to
start nuclear fusion. Nuclear fusion is the process of combining nuclei to form a new, larger nucleus. This
section will go through the process of converting hydrogen into helium by the pp cycle.
Hydrogen is converted into helium in three steps. The final result is that four protons have combined to
form one helium nucleus.
4 11 → 4 + 2 +01 + 2 + 2
2
Four protons join together and fuse, to produce one helium nuclei along with two positrons, +01 , two
neutrinos, , and two gamma rays, .
This does not mean that four protons join at one time, instead the reaction occurs as shown in the following
steps.
Step A
proton positron +01
P deuterium We write this as: 2 11 → 2 + +01 +
1
P
N
neutrino
P
proton
Note:
A gamma ray is a high energy, short wavelength, electromagnetic wave.
A positron is a positive electron. It is the antiparticle or antimatter counterpart of the electron.
A neutrino is a subatomic particle that has no electric charge and a very small mass, which might
even be zero. Neutrinos are one of the most abundant particles in the universe. Because they have
very little interaction with matter, they are very difficult to detect.
12 Module 8 From the Universe to the Atom
Step B Helium-3 11 + 12 → 3
deuterium 2
P
P P
N
N
P
P proton 3 + 3 → 4 +2 11
proton 2 2 2
Step C N
P Note: the reaction here refers to nuclei. We do not
Helium-3 have electrons. Helium-4 is also called an alpha
P particle.
P N
P
Helium-4
N
P proton
P
P
N
Helium-3
Simulation stellar nucleosynthesis
Introduction
To try and make the preceding work more realistic try the following:
Part A
In part A two protons combine. In doing so one of the protons converts into a neutron by losing a positron
(a positive electron) and a neutrino. This changes one of the protons into a neutron and allows the two
particles to combine as there is no electrostatic repulsion to form a deuterium nucleus.
2 1 → 2 + +01 +
1 1
The following is required:
Coloured cotton balls or coloured marshmallows, etc., glue stick, a sheet of A3 paper.
Use the location given in the steps above for details on where to glue the balls.
Use a white ball for the protons and a coloured ball for the neutrons. Glue these on the A3 paper and draw
in the positron and the neutrino to represent the reaction for part A.
Module 8 From the Universe to the Atom 13
Part B
In part B a proton combines with a deuterium nucleus (produced in part A). This new nucleus will now
have 2 protons and 1 neutron and represents a Helium-3 nucleus.
On the A3 paper glue the white and coloured balls to represent hydrogen (1 proton) and deuterium (one
proton, one neutron). After they combine, their product can be represented by 2 protons and 1 neutron
(Helium-3 nucleus).
Part C
The nucleus from part B is a Helium-3 nucleus. In part C, two Helium-3 nuclei combine to form a Helium-
4 nucleus and release 2 protons.
On the A3 paper, glue the white and coloured balls in the proper locations. The two reactants should be
Helium-3 nuclei, with 2 protons and 1 neutron each. The product of this reaction is a Helium-4 nucleus and
two protons.
Overall this reaction is represented by 4 11 → 4 + 2 +01 + 2 + 2
2
Larger mass main sequence stars
The carbon-nitrogen-oxygen (CNO) cycle is the main type of nuclear reaction in higher mass, hotter
main sequence stars. The coulombic repulsion is much greater due to the larger charge and this is why a
larger mass star is necessary as it has a greater temperature at the core, so being able to overcome the
coulombic repulsion. It also converts four protons into one helium nucleus but does so by a different
process.
Four protons combine with a carbon nucleus to produce - nitrogen, then oxygen and finally carbon again
plus a helium nucleus, that is: 4 11 + 162 → → → 24 + 162
This process is cyclic, as a carbon nucleus is present both at the start and at the end, and can start the process
again. Because of this we say that carbon acts as a catalyst in the fusion of hydrogen into helium.
We can represent this with the following diagram.
Credit: http://astro.unl.edu/classaction/sunsolarenergy.html
14 Module 8 From the Universe to the Atom
After the main sequence (also called post main sequence)
In post main sequence stars there is a lot of helium in the core allowing three helium nuclei to fuse to form
a carbon nucleus through a triple-alpha reaction. This process occurs when the star is in the red giant stage.
When the core is mainly carbon, the star contacts causing the temperature to rise further and helium to fuse
with carbon to produce oxygen. Further shell-burning reactions take place in successively deeper shells
within the star, converting carbon to neon and magnesium, oxygen to silicon and sulfur, and silicon and
sulfur to iron. A diagram showing these shells is shown below.
Credit: Penn State Astronomy & Astrophysics
Note: we discuss red giant stars later in this module.
Supernovae
Beyond iron the nuclear reactions stop because, unlike the previous reactions, energy is required. This
causes the force pushing on the outer layers of the star to decrease and gravity causes the outer layers of
the star to rush towards the core of the star at very high speed. This releases a lot of energy and the star
explodes, which is known as a supernova. When these massive stars explode elements heavier than iron
such as gold and uranium are produced.
Sample problem 8.2
In a fusion reaction the total mass of the particles before the reaction is 6.684 × 10-27 kg and after the
reaction 6.680 × 10-27 kg. Calculate the energy released.
Solution:
m = 6.684 × 10-27 6.680 × 10-27 = 0.004 x 10-27 kg
The energy released is calculated from E = mc² = 0.004 x 10-27 x (3 x 108)2 = 3.6 x 10-13 J.
As 1 eV = 1.602 x 10-19 J then this gives the energy released as 2.25 MeV.
Module 8 From the Universe to the Atom 15
Question sheet 8.2
1. An alpha particle is represented by 42 . How many protons and neutrons are in an alpha particle?
2. What element is represented by 2 ? How many protons and neutrons does it have?
3. The curiosity rover, a robotic probe, which landed on Mars in 2012 is powered by heat from radioactive
decay. The radioisotope used is 234 which decays to 2324 . Write a balanced nuclear equation for this
reaction showing the type of radioactive decay occurring.
4. Using the masses given in the following table calculate the energy released in the reaction in question 3
above.
particle mass (u)
234 238.049553
2324 234.040950
42He 4.001506
5. A star has a luminosity of 3.9 × 1026 W. How much mass does the star convert to produce this amount
of energy every second?
6. A star with a luminosity of 3.8 x 1026 W changes 3 × 1025 kg of mass into energy during the main part
of its lifetime. Calculate the time in years for this to happen.
7. The sun is a main sequence star. Describe two types of nuclear reactions that occur in main sequence
stars.
8. Describe the nuclear reactions that occur in red giant stars.
16 Module 8 From the Universe to the Atom
The origin of spectra
Continuous spectra
A continuous spectrum has all wavelengths present. It is usually produced by hot solids, for example, a
tungsten filament light globe. The electrons in the hot metal can exist at all possible energy levels and hence
all possible electron movements can occur which produces all wavelengths, known as a continuous
spectrum.
Emission spectra
In an atom, the electrons which move around the nucleus have fixed energy levels. If the electrons are in
the lowest possible energy level, the atom is said to be in its ground state. The electrons may be in other
higher energy levels, when the atom is said to be in an excited state. An emission spectrum is produced
when electrons are excited to move up to energy levels where they are unstable and on falling towards the
nucleus and becoming more tightly held to the nucleus, give off energy. This energy is in the form of a
photon of light, the smallest possible packet or quantum of light of a given wavelength. This is illustrated
in the diagram below.
Electron in a high energy orbit
The electron falls back to a lower energy level and photon of light is
energy is emitted in the form of light. The bigger emitted
the drop, the greater the energy emitted and the
shorter the wavelength of light. Electron in a lower energy orbit
A diagram of an emission spectra is shown below. This consists of bright coloured lines on a dark
background. Colours of higher frequency, that is shorter wavelength, are produced when a greater energy
movement occurs.
Module 8 From the Universe to the Atom 17
Absorption spectra
As you saw in module 7 when looking at reflected sunlight through a spectroscope a continuous spectrum
with vertical dark lines was observed, which is an absorption spectrum.
An absorption spectrum is produced when electrons take in energy from a beam of white light causing
them to move further from the nucleus. This absorbed energy is what produces the dark lines in the
spectrum.
The electron absorbs a photon of light and gets
pushed up into a higher energy orbit.
Excited electron
Photon of light is Electron in a lower energy orbit
absorbed by the
electron.
A diagram of an absorption spectra is shown below. This is a continuous black body spectrum on top of
which are dark lines. Note the emission and absorption lines for the same element have the same
wavelength, that is they are in the same place, they are the negative of each other.
Key features of stellar spectra
Stars are similar to black bodies so their spectrum is that of a black body corresponding to the temperature
of the star s surface. There are also dark absorption lines produced because of light passing through the
star s cooler atmosphere, that is above its surface. The electrons in the atoms of the star s atmosphere absorb
energy and consequently remove specific colours of light. For this reason, stars are observed to produce
absorption spectra similar to that shown below.
Spectrum of a star showing absorption lines
18 Module 8 From the Universe to the Atom
Information which can be obtained from spectra
Spectra is used to provide nearly all the information that is available on stars.
Surface temperature of a star
The continuous spectrum of a star is similar to that of a black body of the same surface temperature. By
plotting the intensity of a star s radiation against wavelength, the wavelength at which intensity is a
maximum can be found. Wien s law shows that this wavelength is inversely proportional to the surface
temperature in kelvin of the star. You may need to review Wien s law in module 7 - the nature of light.
In order to calculate the surface temperature of the star from the wavelength of maximum intensity you use
Wien s law equation: m = where b = 2.89 x 10-3 m K.
Find the wavelength of maximum intensity for the following temperatures:
4000 K
6000 K
8000 K
10000 K
Short wavelength light is blue and long wavelength light is red. Therefore, blue stars are the hottest, with
surface temperatures around 10000 K, yellow-white are medium temperatures with surface temperatures
around 6000 K and red are the coldest, with surface temperatures around 3000 K.
The Doppler effect
In module 3 - waves and thermodynamics, we investigated the Doppler effect for sound. The Doppler effect
also occurs with light and is important in measuring many characteristics of stars. Review the following
video, search YouTube for Classroom Aid - Do le Effec . Summarise what the Doppler effect can tell
you about the properties of stars.
Introduction to spectroscopy
Review the following video, search YouTube for Spectroscopy - Splitting the Starlight Max Planck
Socie . Summarise what spectroscopy can tell you about the properties of stars.
Module 8 From the Universe to the Atom 19
Translational velocity - the star is moving
The translational velocity of a star parallel to an observer can be measured by observing the amount and
direction of Doppler shift shown by the star s absorption lines. If a star is approaching the observer, every
absorption line in the spectrum of the star is shifted toward the blue end of the spectrum. If the star is
moving away all the lines are shifted towards the red end. The amount by which all the lines are shifted
depends on the component of the velocity of the star along the line of sight, known as the translational
velocity. The diagram below illustrates this red-shift in the spectrum.
star not
moving
star moving away
from us
the doppler shift the doppler shift
Note: the amount of red shift shown above is exaggerated to illustrate the concept.
Chemical composition
As we saw in module 7 the nature of light, each chemical element has a unique emission spectrum
consisting of lines corresponding to the electron movements within the element. This is what we observed
when looking at the spectra from discharge tubes or some street lights. These lines are in the same place as
the lines in an absorption spectrum. Elements in the star s outer layers absorb light from the continuous
black body spectrum from the core of the star. A comparison of a star s absorption spectrum with the spectra
of known elements allows the chemical composition of the star s outer layers to be found.
Classifying of stars by their stellar spectra
A stellar spectrum is made up of a black body curve for the temperature of the star s surface, on top of
which are absorption lines from the elements that are in the star s atmosphere. The shape of the graph of
intensity against wavelength and the position of the intensity maximum, tells us the surface temperature of
the star. When stars of different surface temperature are compared, there is an increase in luminosity along
with a gradual change from red, for the coolest stars, through orange, yellow, white and eventually to blue
for the hottest stars.
This means that spectra can be used to classify visible stars into several spectral classes which are labelled:
O, B, A, F, G, K, and M, from hottest to coolest. Each spectral class has a characteristic colour and surface
temperature range, and each is characterised by specific absorption line patterns, indicating the elements in
the star s atmosphere.
Table of spectral classes of visible stars
Spectral Class Colour Surface temperature (K) Elements present in absorption lines
O blue 28,000 50,000
B blue-white 10,000 28,000 ionised Helium
A white 7,500 10,000 neutral Helium
F white-yellow 6,000 7,500
G yellow 4,900 6,000 strong Hydrogen
K orange 3,500 4,900 weak ionised Ca+
M red 2,000 3,500 ionised Ca+, metals
ionised Ca+, Fe, strong molecules
strong molecules such as TiO
20 Module 8 From the Universe to the Atom
You should notice that very hot stars, class O, have enough energy to ionise helium. Cooler stars such as
M class have molecules in their atmosphere. Hotter stars do not have molecules as their temperature would
break the bonds holding the molecules together.
Mnemonic
A mnemonic is a method we use to remember things. For spectra class we can use this:
OBA F GKM
Oh Be A
Fine Gorilla Kiss Me
Different types of stars
When looking at the night sky we see that stars have different colours some of them appear to be a reddish
colour, most are white and a few are bluish. These different colours (which are directly related to
temperature) are because the stars we see are different in size (mass) and age (different stages of evolution).
An important graph, the HR diagram, was obtained by the astronomers Russell and Hertzsprung. They
plotted luminosity (the energy released per second) against surface temperature (colour).
Note:
Another measure of luminosity which we use in the following practical investigation is absolute magnitude
(M) this is a scale where the more negative the values then the more luminous the star.
Another measure of temperature is the spectral class of the star, OBAFGKM, but in this case each letter in
the spectral class list is subdivided into 10, numbered 0 to 9, to make smaller divisions between stars. This
means that an F5 star is slightly hotter than a F6 star. Take care - the temperature scale has temperature
going from hot to cooler the reverse of what we normally expect when drawing graphs.
Practical investigation the Hertzsprung Russell (HR) diagram
The H-R diagram shows the relationship between a star's luminosity, (or absolute magnitude) and its
surface temperature (or spectral class).
Absolute magnitude (M)
Absolute magnitude (M) is a measure of the amount of light a star radiates into space, which is, a measure
of the star s luminosity. It is defined as the brightness the star would have to an observer at a fixed distance
of 10 parsecs from the star.
The astronomers, Hertzsprung and Russell, worked out that there was a connection between luminosity (or
absolute magnitude) and surface temperature (or spectral class) when you graph these quantities. Their
diagram helped astronomers organize stars into different groups (this is similar to what the periodic table
of the elements does for Chemists).
The next page lists some of the brightest stars and some of the nearest stars in the sky. You need to fill in
the Spectral Type for each star using the program Stellarium which is free and available for download
from https://stellarium.org
To do this run Stellarium and then:
Search and select each star in the following list by opening the search window and typing the letters
HIP and then the Hipparcos catalog number, and then pressing Enter to select and center the star and
display the information on the star.
In the information that appears on screen, the star's Absolute Magnitude is listed on the third line of
information, and its Spectral Type is listed on the 7th or 8th line from the bottom. Note the position of
the information varies depending on the version of Stellarium you are using.
Use this information to fill in the blanks in the table. Keep only the first UPPER CASE letter and the
following number in the Spectral Type listing ignore any roman numerals or letters after the
numbers. Note that a few stars have already been entered for you.
If you need help with Stellarium then look on YouTube for a video, for example, Stellarium: Getting
a ed . You may decide to work together in groups to speed up this investigation.
Module 8 From the Universe to the Atom 21
Caution makes sure you enter ABSOLUTE magnitude. Get your teacher to check a few of your values.
Give the absolute magnitude values to 1 decimal place only.
Nearby Stars Bright Stars
# Star name Hipparcos Spectral Absolute # Star name Hipparcos Spectral Absolute
Catalog Type Magnitude Catalog Type Magnitude
Number Number
1 Proxima 70890 26 Sirius A 32349
2 Alpha Centauri A 71683 27 Canopus 30438
3 Alpha Centauri B 71681 K1 5.6 28 Rigel Kentaurus 71683
4 Barnard's Star 87937 29 Arcturus 69673
5 Kapteyn's Star 24186 30 Vega 91262
6 Lalande 21185 54035 31 Capella 24608
7 Sirius A 32349 32 Rigel 24436
8 BD+68 946 86162 M3 10.9 33 Procyon 37279
9 Wolf 1061 80824 34 Achernar 7588
10 Kruger 60 A 110893 35 Betelgeuse 27989
11 Ross 154 92403 36 Hadar 68702
12 Van Maanen 2 3829 A2 14.1 37 Acrux 60718
13 Epsilon Eridani 16537 38 Altair 97649
14 Ross 128 57548 39 Aldebaran 21421
15 Luyten's Star 36208 40 Antares 80763
16 Epsilon Indi 108870 41 Spica 65474
17 61 Cygni A 104214 42 Pollux 37826
18 61 Cygni B 104217 43 Fomalhaut 113368
19 Procyon A 37279 44 Mimosa 62434
20 Lacaille 8760 105090 M1 8.7 45 Deneb 102098
21 Groombridge 34 1475 46 Regulus 49669
22 Lacaille 9352 114046 47 Adhara 33579
23 Tau Ceti 8102 48 Castor 36850
24 Ross 614 A 30920 49 Gacrux 61084
25 Luyten 725-32 5643 M6 14.3 50 Shaula 85927
Plot each star's Absolute Magnitude on the y-axis and its Spectral Type on the x-axis. Each star will be a
dot somewhere on this graph. Notice that one star is already plotted, the sun which is a Spectral Type G2
star, with an absolute magnitude of 4.8. Following this example, plot the rest of the stars on the graph. Do
this in pencil.
22 Module 8 From the Universe to the Atom
absolute magnitude - 15
-10
-5
0
5
10
OB A
15
Note: spectral type is subdivided into
Module 8 From the Universe to the Atom
FG K M
smaller divisions, that is, 0, 2, 4, 6, 8 spectral type
23
HSC Physics for NSW Study Guide Series
Questions
1. In what part of the diagram are most of the nearby stars plotted: upper left, lower left, upper right or
lower right? .. ..
2. In what part of the diagram are most of the bright stars plotted? . ..
3. Where on your diagram are most of the stars you plotted located? ...
4. Name the hottest star you plotted ...
5. Name the coldest star you plotted ..
6. Name the brightest star you plotted . ..
7. Name the dimmest star you plotted . ..
8. Can you find a star on your diagram that is both bright and cool? What is its name?
9. What part of the diagram is it located in? ..
10. Can you find a star on your diagram that is both hot and dim? What is its name?
............................................................................................................................................
11. What part of the diagram is it located in? ..
12. Are stars with a larger mass generally hotter or colder? .. ..
13. Compare the star Vega to our sun. Is it more or less massive than the sun? Why?
The part of the H-R diagram where most of the stars are plotted is called the Main Sequence. The sun, for
example, is on the Main Sequence. This part of the curve is where stars in the main part of their life are
located as they fuse hydrogen into helium.
Draw a curve through the Main Sequence on your diagram.
14. If a Main Sequence star was type A6 then using your diagram what should its absolute magnitude
be? ..
15. What about a type K4 star? ....
16. What about a type M8? ..................................................................
Are more stars on the Main Sequence or off it? .
..
24 Module 8 From the Universe to the Atom
The Hertzsprung-Russell diagram (The HR diagram)
A Hertzsprung-Russell diagram is a graph of a star s luminosity, (or absolute magnitude), against its surface
temperature, (or spectral class) and shows the connection between luminosity and temperature of stars. The
region of the H-R diagram where a star is found depends on its stage of evolution. Each evolutionary stage
is controlled by the main nuclear fusion processes in the star s centre, these being:
main sequence: H fusion. This is where the star spends most of its lifetime.
red giant: He fusion. The star has used up a lot of hydrogen in its core and now starts fusing helium.
supergiant: The star is massive and the temperature at the core allows other fusion reactions to occur.
white dwarf: The nuclear reactions have stopped leaving the hot core of the star to cool down.
From the location of the star the energy sources characteristic of each evolutionary stage can be identified.
The HR diagram shown below should be similar to what you plotted in the practical investigation.
Credit: Chandra X-ray observatory
Note with the HR diagram axes:
the x axis can be shown as spectral class, temperature or colour as these are all related.
the y axis can be absolute magnitude or luminosity as these are related.
The location of a star on the HR diagram gives you information on its evolutionary stage. A main sequence
star is in the prime of its life. A red giant has used up most of the Hydrogen in its core and is now fusing
helium and is reaching the end of its life. A white dwarf has stopped all nuclear reactions and is slowly
cooling down.
Module 8 From the Universe to the Atom 25
HSC Physics for NSW Study Guide Series
The evolution of stars
Stars form as gas condenses inside huge interstellar gas clouds. These gases contract due to their own
gravitational attraction. The star is then stable for a long time while the hydrogen at its centre is converted
into helium with the release of a very large amount of energy due to Einstein s relationship, E = mc2. This
stage is the main sequence stage on the HR diagram. Most stars lie on the main sequence with their location
dependant on their mass when formed.
The more massive a star is the quicker it uses up its hydrogen and hence the brighter, bigger, and hotter it
is. Therefore, when looking at the HR diagram the stars higher up on the main sequence are hotter and more
luminous. The quick conversion of hydrogen into helium also means that the hydrogen gets used up quicker
for the massive stars than for the lighter ones. For a star like the sun the main sequence stage lasts about 10
billion years whereas a star 10 times as massive will be 10000 times as bright but will only last for 100
million years. The reverse is also true, a star the tenth the mass of the sun will have a lifetime far greater
than the current age of the universe.
Main sequence stars
In main sequence, lower mass stars, the pp cycle is the predominant reaction while in larger mass stars it is
through the CNO cycle. This means that stars are losing mass all the time as mass gets converted into
energy such as electromagnetic radiation which gets radiated into space.
Supergiant stars
In supergiant stars the same process occurs, but the reaction produces Carbon, Nitrogen and Oxygen.
Giants or red giants
As stars evolve, they move very slightly up the main sequence; the bigger they are the faster they burn
hydrogen. Finally, most of the hydrogen at the centre is converted to helium and this helium collapses in
on itself, reacting to form heavier elements. This produces so much energy that the outer hydrogen burning
shell expands outwards, forcing the star to grow to very large sizes, which we call giants or red giants. The
outer surface of the star is cooler, appearing red. The star hence moves off the main sequence onto the red
giant stage.
White dwarfs
With a low or medium mass star, the burnt-out star will collapse in on itself to produce a white dwarf made
of mainly C, N, and O where nuclear reactions have stopped. You will notice looking at the HR diagram
that a white dwarf can have the same temperature as a main sequence star but is not as luminous. This is
because the white dwarf has a much smaller surface area.
Supernova
If the mass is greater than about 5 - 8 solar masses, the heavier elements in the centre start to react and iron
is produced in the centre of the star. The iron is stable and produces no energy so the star quickly collapses
in on itself, going from a radius of 8000 km to 20 km in approximately one second. The core then bounces,
forming heavier elements that are ejected into space, along with the energy of about one billion stars, which
lasts for about one month. Thus, the star has become a supernova. Supernova are not shown in the HR
diagram.
The first stars
The first stars formed after the big bang were composed almost entirely of hydrogen and helium, without
oxygen, nitrogen, iron, or any of the other elements. These larger elements were all produced inside massive
stars and then spread throughout space by supernova events. We are made up of material that has been
processed at least once, and probably several times by stars.
26 Module 8 From the Universe to the Atom
Question sheet 8.3
1. Consider two main sequence stars, Proxima Centauri and Vega. Proxima Centauri has a mass of 0.12
solar masses and Vega has a mass of 2.6 solar masses.
(a) Which star contains more hydrogen to fuse into helium? .
(b) Which star will run out of hydrogen first and so leave the main sequence first? ..
(c) Which star is producing more power and is more luminous? Explain your answer.
(d) What do you think is the connection between a star s luminosity and its lifetime for main sequence
stars?
2. Complete the table below.
Colour of star Temperature (hotter or cooler) Luminosity (higher or lower)
Bluer
Redder
3. Inside the core of stars like the sun, hydrogen nuclei fuse together to form heavier nuclei.
(i) What is the name of the region of the Hertzsprung-Russell diagram in which stars like the sun are
located? .
(ii) One type of fusion reaction is the proton-proton chain and is shown below.
6 1 → 4 + 2 +01 + 2 1 + 2 + 2
1 2 1
What particles are represented by the letters X and Z. ..
4. Outline what will happen to a star similar in size to the sun to make it leave the main sequence.
5. Outline what will happen to a star for it to become a supernova.
6. Your blood contains iron. Outline where this iron came from.
Module 8 From the Universe to the Atom 27
HSC Physics for NSW Study Guide Series
7. The following graph is of a Hertzsprung-Russell diagram.
(a) The labels on the axes of the Hertzsprung-Russell diagram are missing. What should they be?
Horizontal axis ................................................................ Unit ..................................................
Vertical axis ....................................................................
(b) One of the axes can also be shown as the colour of a star. On the diagram label this axis with the
colours blue and red.
(c) What is the relationship between the colours and the numbers on this axis?
(d) On the HR diagram, put a circle around the region that stars produce most of its energy by the pp
cycle. Label this circle pp.
(e) On the HR diagram, put a circle around the region that stars produce most of its energy by the CNO
cycle. Label this circle CNO.
(f) On the HR diagram, put a circle around the region where stars have stopped all nuclear reactions
and are just cooling down. Label this circle no nuclear reactions.
8. Before Einstein s relationship, E = mc2 it was thought that stars produced energy by gravitational
collapse which meant that the life was much shorter than our current understanding. Outline how
Einstein s relationship explains the energy source in stars on the main sequence.
.
.
28 Module 8 From the Universe to the Atom
Inquiry question: What evidence is there for the origins of the elements?
Now that you have covered this section you should be better able to answer the inquiry question with your new
understanding of the origins of the elements.
Summary
Write a summary of origins of the elements, review your summary with others in the class, update as
necessary.
.
.
.
.
.
.
.
.
.
.
Module 8 From the Universe to the Atom 29
HSC Physics for NSW Study Guide Series
Structure of the atom
Students:
investigate, assess and model the experimental evidence supporting the existence and properties of the
electron, including:
- early experiments examining the nature of cathode rays
- Thomson s charge-to-mass experiment
- Millikan's oil drop experiment (ACSPH026)
investigate, assess and model the experimental evidence supporting the nuclear model of the atom, including:
- the Geiger-Marsden experiment
- Rutherford s atomic model
- Chadwick s discovery of the neutron (ACSPH026)
NSW Physics Stage 6 syllabus © NSW Education Standards Authority for and on behalf of the Crown in right of the State of New South
Wales, 2017.
Inquiry question: How is it known that atoms are made up of protons, neutrons and electrons?
With all inquiry questions consult with class members, come to a consensus and then summarise your answer in the
space provided.
30 Module 8 From the Universe to the Atom
Risk assessment
Before using cathode ray tubes, a risk assessment needs to be carried out.
Risk assessment cathode ray tubes
Activity Observation of low-pressure gases when an electric field is applied.
Hazard High voltage power supplies and 230 V power cable. Implosion of glass
tubes.
Hazard information Coming into contact with high voltage, flying glass and X-rays from some
high voltage sources.
Summary of activity
A high voltage power supply is connected to cathode ray tubes containing air under low pressure.
Observations are made of the gas in the tubes.
Risk identification
Contact with 230 volts and the high voltage side of the power supply. X-ray exposure. Flying glass if the
tubes should get damaged and break.
Discuss with your class where you think the ticks should go.
Likelihood very likely likely unlikely very unlikely
(tick box)
Consequence extreme major moderate minor
(tick box)
Control
230-volt cable checked to make sure it has no damage. If possible, replace high voltage supplies which
use induction coils as these can produce X-rays. A suitable alternative is a current limited 5 kV power
supply.
Take care not to damage the glass tubes causing them to break.
Write a conclusion about the risk in the space below.
Conclusion
about risks
Student involved in assessment:
Name of Assessor: .
Signature: . Date:
(of assessor)
Note the assessor is your teacher who has discussed with you and approved the risk assessment.
Module 8 From the Universe to the Atom 31
HSC Physics for NSW Study Guide Series
The electron
Early experiments examining the nature of cathode rays
With the development of an improved vacuum pump the stage was set for investigations with low pressure
gases. The conduction of electricity through gases at low pressures led to the discovery of cathode rays
which we now know are electrons.
Practical investigation low pressure tubes
A common piece of equipment found in schools is a set of six glass tubes containing air at different
pressures. A high voltage is connected across the tubes in turn and observations made.
Describe with the help of diagrams the observations you made.
You should notice that different pressures produce different observations. At high pressure there may not
be much to observe and then as the pressure decreases patterns will form. At very low pressure you may
observe the glass tube glowing.
As an alternative or preparation for the practical investigation above watch the following YouTube video,
search for Ca hode Ra Lead o Thom on' Model of he A om, Ve i a i m . Open
Answer the following questions
Who was Geissler and what was his importance to the discovery of cathode rays? (you may have to search
further for this information).
What charge does the cathode electrode have? . .
What were the two main theories regarding the passage of electricity through the gas?
What did J.J. Thomson conclude in 1897?
32 Module 8 From the Universe to the Atom
Typical observations
At low pressures the following observations are made:
anode
bright
positive column
(striated)
high voltage
Faraday s dark space negative glow
to vacuum pump cathode
Crooke s dark space
What is happening
Positive ions in the low-pressure air are accelerated by the electric field and hit the negative terminal (the
cathode) causing it to release electrons, that is cathode rays. The cathode rays produced move with
increasing speed towards the positive anode and collide with molecules of the gas causing ionisation which
produces the negative glow. However, before they reach the region of the negative glow, they do not have
enough energy to produce ionisation and so no light is produced. This is known as Crooke s dark space.
The electrons lose energy because of collisions in the negative glow and so do not have enough energy to
cause ionisation. This produces Faraday's dark space. The electrons now have enough energy to cause
ionisation in the positive column. The striations are because:
ionisation of the gas occurs producing light
the electrons now have lost energy so they cannot produce ionisation
the electrons next speed up
ionisation of the gas occurs once again producing light.
The glass glow
At very low gas pressure the gas glow nearly disappears and parts of the wall of the glass tube start to
fluoresce, that is give off light. The fluorescence is caused by the cathode rays hitting the glass. The colour
of the fluorescence depends on the impurities in the glass, it does not depend on the gas in the tube. It was
discovered that the fluorescence could be moved to different parts of the glass by placing a magnet close
to the tube. This means that a magnetic field can deflect cathode rays.
Module 8 From the Universe to the Atom 33
HSC Physics for NSW Study Guide Series
Schools often have a variety of cathode ray tubes which your teacher may show you or as an alternative
you can view the following YouTube videos.
The Maltese cross discharge tube and the fluorescent screen
Search for Maltese cross.avi Open and also HSC Study Lab: Y12 Physics: Cathode rays . Open
Summarise your observations with the following table:
Diagram of tube Observations What this tells you about
The Maltese cross tube cathode rays
Paddle wheel tube
34 Module 8 From the Universe to the Atom
The cathode ray tube containing electric plates
As we saw in module 7, cathode rays can be deflected by electric fields with the following equipment.
electric field pair of metal plates
accelerates
electrons metal can with
hole
heated filament
low voltage voltage for metal plates
electron gun
vacuum
0 5 kV
high voltage for
electron gun
phosphor screen glass tube
If the top metal plate is made negative what direction does the cathode ray move? Note this is analogous to
the motion of a projectile in a gravitational field. ..
What properties of cathode rays are found from this experiment? .
What is the sign of the charge on the cathode ray? .
The cathode ray tube and the magnetic field
Magnetic fields can be applied by different methods. The simplest is to use a bar magnet however another
method is to use Helmholtz coils. A Helmholtz coil, named after the German physicist von Helmholtz,
produces a region of nearly uniform magnetic field.
If you use Helmholtz coils then a low voltage DC supply is required. If you use a normal school power
supply then it helps to smooth the output DC voltage with a large value capacitor in parallel with the voltage
supply.
If a magnetic field is applied out of the page in the diagram above what direction will the cathode ray move?
.
What properties of cathode rays are found from this investigation?
.
Identify the sign of the charge on the cathode ray and explain how you found this.
.
Summary
Explain what we know about electrons from these investigations.
Module 8 From the Universe to the Atom 35
HSC Physics for NSW Study Guide Series
Thomson s charge-to-mass experiment
The physicist JJ Thomson in 1897 used the property that electrons can be deflected by electric and magnetic
fields to measure the charge to mass ratio (q/m) of the electron. This value showed that electrons were much
smaller in mass than the smallest atom, hydrogen, and hence were a fundamental part of all atoms.
The diagram below shows Thomson s arrangement for the deflection of cathode rays in an electric field.
An electric field was applied across the two plates and it was observed that the cathode rays were deflected
indicting that they had negative charge.
From: Clarke Chemistry - the story of the atom
Your teacher may show you an experiment with a cathode ray tube and crossed electric and magnetic fields,
that is electric and magnetic fields at 900 to each other.
The following YouTube videos can be used as preparation or as an alternative to the experiment. Search
YouTube for Physics Lab Demo 7: Thomson Experiment Open and also Discovery of the Electron:
Cathode Ray Tube Experiment: Open
Describe the experiment with the vacuum tube (Teltron tube), and the coils (Helmholtz coils), to simulate
Thomson s experiment.
36 Module 8 From the Universe to the Atom
To understand what is happening we need to look at the influence of magnetic and electric fields on cathode
rays.
Cathode rays in a magnetic field e
Electrons in a magnetic field experience a force that causes them to move
in a circular path. The force on the electron is at right angles to its motion.
This is what happens with circular motion. Thus, if the electron is
travelling perpendicular to a uniform magnetic field, it follows a circular
path, and the magnetic force on the electron is equal to the centripetal
force. This is shown in the diagram opposite. Look at the electron s
movement at its current location. Using the right-hand palm rule, place
your right-hand flat on the page. The thumb points against the electrons
motion. Your fingers point in the magnetic field direction, that is up the
page. The force on the electron is into the page at 900. This force is always
into the centre of the circle, that is it is centripetal motion.
The centripetal force is produced by the magnetic force.
Fc = FB =
2 = or
Looking at the relationship = we see that if the velocity of the charged particle increases then the
radius of curvature gets larger, that is it bends less.
Cathode rays in an electric field ---------
If the particle is moving initially at right angles to the field as shown
opposite, then the force will cause an acceleration parallel to the field. This -
is similar to the trajectory of projectile motion where the gravitational field
acts at right angles to the motion of a projectile. An electron as it is
negatively charged will be deflected towards the positive plate.
The electric field strength E is given by E = F/q.
This gives the electric force FE =qE.
+++++++++
-
Module 8 From the Universe to the Atom 37
HSC Physics for NSW Study Guide Series
Calculating the velocity of cathode rays
Thomson calculated the velocity of the cathode ray as follows:
Cathode rays were passed through an electric field crossed at right angles by a magnetic field. This is
illustrated in the diagram below.
negative plate
stream of magnetic field out of page
cathode rays produces force upwards
of velocity v
electric field up the page produces
force downwards
positive plate
The cathode rays are attracted towards the positive plate with a force FE = qE, however, the magnetic field
gives a force in the opposite direction of size FB = qvB.
If the net force is zero then FE = FB and there is no deflection of the cathode rays.
qE = qvB hence we get: =
If we know B and E, then we can calculate the velocity of the cathode rays.
Once Thomson had a value for the velocity of the cathode ray, = , he switched off the electric field and
measured the radius of curvature of the cathode ray when it experienced a magnetic field only.
Solving the equations
The magnetic force provides the centripetal force hence = 2
Substituting the velocity of the cathode ray into this equation we get:
2
= ℎ = =
= ℎ = =
2
E can be calculated from , r can be measured and B can be measured.
From these figures, Thomson was able to calculate a value for the charge to mass ratio (q/m) of the cathode
rays.
He found that the value of q/m for the cathode ray was much larger than q/m for the hydrogen ion. Thomson
made a rough measurement of the charge on the cathode ray and found it to be similar to that of a hydrogen
ion.
As the charge on the hydrogen ion is approximately the same as the cathode ray this meant that the mass
of the cathode ray was much smaller that the smallest known atom hydrogen. As the hydrogen atom was
thought to be the simplest atom, this meant that these cathode ray particles were smaller than atoms.
38 Module 8 From the Universe to the Atom
Sample problem 8.3
Two metal plates separated by 1.00 cm have a potential difference of 4.00 kV applied across them. A
uniform magnetic field of size 20.0 mT is applied perpendicular to the plates so that an electron moving
perpendicular to both fields experiences no net force.
(a) Show in a diagram the relative orientation of the electric field, the magnetic field, and the direction of
the electron.
(b) Calculate the speed of the electron.
(c) What is the radius of the electron orbit when the electric field is removed?
Solution:
(a) One possible arrangement is that the electric field is down the page, the magnetic field is into the page
and the electron travels from left to right in the plane of the page. This with the appropriate values of
E and B can produce no net force, that is the electron will travel in a straight line.
electron ++++++++
xxxxxxxxx
xxxxxxxxx
--------
(b) = = 4.00 x 103/1.00 x 10-2 = 4.00 x 105 V m-1. The speed of the electron is found from = =
4.00 x 105/20 x 10-3 = 2.0 x 107 m s-1.
(c) = m 2 or = m = .10 10−31 2.0 10 = 5.69 x 10-3 m.
1.602 10−1 20 10−3
r
Question sheet 8.4 charged particle ++++++++
1. A charged particle is travelling in a straight line xxxxxxxxx
xxxxxxxxx
between two parallel charged plates and a magnetic
field. The magnetic field is 0.015 T and is directed in
towards the page. The parallel charged plates are 1.5
cm apart and have a potential difference of 180 V.
Calculate the velocity of the particle.
--------
2. For an electron in a cathode ray tube, eV = ½ mv2. Explain what the term eV refers to.
3. In a cathode ray tube, electrons are accelerated through 28 kV. Calculate their speed.
Module 8 From the Universe to the Atom 39
HSC Physics for NSW Study Guide Series
4. Electrons are accelerated from rest through a voltage of 3500 V in an evacuated tube. Then, they enter
a uniform magnetic field B of strength 2.5 x 10-3 T at right angles to the electron beam.
(a) Calculate the speed of the electrons on entering the magnetic field.
(b) Calculate the size and direction of the force experienced by an electron in the magnetic field.
(c) Explain why the electrons move in a circular path and calculate the radius of this path.
5. Outline the early experimental evidence examining the nature of cathode rays.
6. (a) Draw a labelled diagram showing the deflection of an electron by electric and magnetic fields.
(b) Explain why these forces act in the direction you have shown.
40 Module 8 From the Universe to the Atom
Millikan s oil drop experiment
This experiment was first done by Robert Millikan in 1909 and measured the charge on an electron.
Millikan used small charged droplets of oil in an electric field to measure the charge on the oil droplets and
discovered that the charges were all multiples of one number, the charge on an electron. Your school may
have this equipment or as an alternative search YouTube for the following: A Level Physics - Millikan's
Oil Drop Experiment . Open
Watch the video and complete the following:
Draw a labelled diagram of the experimental apparatus.
What does the atomiser produce when it is operated?
What does friction do to the oil droplets?
What charge did the oil droplets gain?....
Force on oil drop (weight) Fg = mg
Force on oil drop (electric) FE = qE where q is the charge on the oil drop
If the oil drop is stationary, the gravitational force = electric force hence mg = qE
m can be measured note: the video at about 6 minutes goes into more depth that we require on the
measurement of mass.
g is known
= which can be measured
From these measurements Millikan found out that the charge on the oil drop, Q, was always a multiple
of 1.6 x 10-19 C. From this we can conclude that the charge on an electron is 1.6 x 10-19 C.
Module 8 From the Universe to the Atom 41
HSC Physics for NSW Study Guide Series
Practical investigation Millikan s oil drop
Search the Internet for the simulation Millikan Oil Drop Lab - The Physics Aviary. Open
This simulation goes through the steps to find the charge on an oil droplet and from this find the charge on
the electron.
Run the simulation taking measurements, recording them in a table in the space below. Work with other
members of your class to tabulate more results.
Table of results
Analysing your results:
One possible method to analyse your results is to use a number line such as that given below. Plot with a
cross the values you obtain.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
What conclusion can you draw from the results you have plotted on the number line? x 10-18 C
42 Module 8 From the Universe to the Atom
The nuclear model of the atom
Thomson, who had worked out that cathode rays were smaller than the smallest atom, produced a model of
the atom which was named the plum pudding model. Rutherford decided to test Thomson s model, and
asked two scientists, Geiger and Marsden to carry out the work.
The Geiger Marsden experiment
The experimental arrangement is shown in the diagram below. The experiment was carried out in a vacuum
to avoid issues such as alpha particles being absorbed by the air.
gold foil some particles are deflected through
large angles
Alpha source
most particles have little deflection
a small number of particles
are deflected through very
large angles
Alpha particles were arranged to hit a thin sheet of gold as shown in the diagram above. As expected, nearly
all the alphas went straight through, but about 1 in 8000 were deflected through large angles. We can
investigate the nuclear models of the atom, that is Thomson and Rutherford s models, with the following
PhET simulation.
Practical investigation Rutherford scattering
Use the PhET Rutherford Scattering simulation. Open
Section 1 - Rutherford Atom
Open the simulation and set the number of protons to 20, then click on the blue button above the alpha
particles to start firing alpha particles towards the gold foil.
(a) Click on the traces button. What do you notice about the paths of most of the alpha particles?
(b) Increase the number of protons to 60. Does it change how the alpha particles move? If so, how?
(c) Now, increase the number of protons to 100. How does this increase change the movement of alpha
particles through the gold foil as compared to when you started? Why do you think this change
occurred?
(d) Repeat the above steps, but vary how many neutrons are present with the protons. Does this change
how the alpha particles travel? Why or why not?
Module 8 From the Universe to the Atom 43
HSC Physics for NSW Study Guide Series
(e) Click on the red/grey sphere and reset the number of protons to 20. Describe with the help of a
diagram how the alpha particles move in relationship to the nucleus.
(f) Now increase the number of protons to 60. Describe with the help of a diagram how the alpha particles
move in relationship to the nucleus.
(g) Now increase the number of protons to 100. Describe with the help of a diagram how the alpha
particles move in relationship to the nucleus.
(h) How are the situations in (e) and (g) different? Why do you think this is?
Plum-Pudding atom that is Thomson s model
(a) Switch the simulation to the Plum-Pudding atom shown at the bottom of the simulation. Once the
simulation opens, click on the trace button. Click the blue button on the alpha particle gun to turn on
the alpha particles. What type of path do the alpha particles take?
(b) How is this different from the Rutherford simulation?
(c) Why do you think the model of the atom changed after Geiger and Marsden s experiment?
44 Module 8 From the Universe to the Atom
Rutherford's atomic model
In Rutherford's model, the positive charge and most of the mass of the atom is concentrated in a small
central nucleus. The nucleus has a radius of about 10-14 m. The electrons orbit the nucleus and explain the
volume of the atom. The atomic radius is about 10-10 m. As can be seen, only a very small number of alpha
particles are deflected through large angles meaning that the nucleus is very small in size. Rutherford was
astonished at the result: It was quite the most incredible event that ever happened to me in my life. It was
as incredible as if you fired a 15-inch hell a a iece of i e a e and i came back and hi o !
Rutherford, after studying the results of the gold leaf, that is the Geiger and Marsden experiment, came up
with a new model of the atom with most of the mass of the nucleus concentrated in a very small volume.
Rutherford did not have any neutrons in the nucleus as neutrons had not been discovered at this time. He
had the same number of protons and electrons to explain why the atom was electrically neutral.
We can visualise this scattering as follows.
alpha particle nucleus
Chadwick s discovery of the neutron Atomic Structure: Discovery of the
As a basic introduction search YouTube for the following video:
Neutron . Open
Summarise the main points below:
Module 8 From the Universe to the Atom 45
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