CHAPTER 9: NUCLEAR & PARTICLE PHYSICS

Graph of N (number of remaining

nucleus) versus t (decay time)

N
No

N = Noe-t

No / 2 T½ = Half-life

No / 4 T½ 2T½ 3T½ 4T½ time, t
No / 8

0

50

Example 9.2.4:

A sample of s31e25cPonodf. mass 4.0 × 10-12 kg emits 4.2 × 107 -
particles per What is the decay constant of ?
32 P
15

Solution 9.2.4:

Mass of 1 mol of 32 P is 0.032 kg. Hence 0.032 kg 32 P
15 15
contains 6.02 × 1023 atoms.

4.0 × 10-12 kg of 32 P = 6.02 1023 x (4.0 × 10-12 kg) atoms
15

0.032

= 7.53 × 1013 atoms

Decay constant of 32 P ,   rate of decay
15 numbers of atoms

  dN dt
N

 4.2 107  5.58107 s1
7.53 1013
51

Example 9.2.5:

Initially, a radioactive sample contains 1.0  106 of
radioactive nucleus. Half-life of the sample is 0T.½5. Find
the number of nucleus that still remains after T½.

Solution 9.2.5: T1  ln 2    ln 2
2
No = 1.0  106 nuclei  T1

from the equation, 2

after t = 0.5 T1 N  Noe- t

2 -( ln 2 )(0.5T1 )
T1

N  Noe 2 2

N  1106 e-0.5 ln 2

N  7.07 105 nuclei left 52

Example 9.2.6:

Thorium-234 has T1 = 24 days. Initial activity of

this particular isotope2source is 10 Ci.

a) How much is the activity of this source after
72 days?

b) How long does it take for the activity to

become 2.5 Ci?

53

Solution 9.2.6:

Given T1  24 days , A0  10Ci

2

a) At t = 72 days

A  Aoet


A  A e 
ln 2  t
T1

2

o

A  10 e  ln 2 (72)
24

A  1.25 Ci

54

Solution 9.2.6:

b) A = 2.5 Ci

A  Aoet


2.5  10 e 
ln 2  t
T1

2

t  24 ln  10 
ln 2  2.5 

t  48 days

55

Example 9.2.7:

The activity of a sample of Radon-222 is 120 Bq. The half-life
of Radon-222 is 3.8 days.
a) What is the decay constant of Radon-222?
b) Calculate the number of Radon-222 atoms in the sample.
c) How many atoms of Radon-222 remain in the sample

when the activity is 40 Bq?
d) How many Radon-222 atoms present after 19 days?
e) Find the activity of the Radon after 19 days.

56

Solution 9.2.7:

a) Using decay constant,   ln 2
T1

2

 ln 2
3.8 day

 1.82 101 day1

 2.11106 s1

b) Using A  dN  N,
dt
 dN
Number of radioactive atoms, No  dt  A



 120
2.11106

 5.69 107 nuclei 57

Solution 9.2.7:

c) Number of Radon-222 atoms remaining, in the sample
when the activity is 40 Bq

N   dN dt



N  40
2.11106

N  1.90107

d) Using N  Noe- t
N  5.69 107 e-(1.82101 day1 )(19 day)
N  1.79106 nuclei left

58

Solution 9.2.7:

e) From

A  dN OR A  Aoe- t
dt N  120e-(1.82101 day1 )(19 day)
N  3.78 nuclei left
A  N

A   ln 2  N
 T1 
2

A  ln 2(1.79106 )
(3.8 24 60 60)

A  3.78 decay s1

59

Example 9.2.8:

One of the usages of radioactive is the
radioactive dating which is a method to
determine the age of a thing base on the rate of
decay and the half-life of the known element.
The half-life of C-14 is known as 5 600 years. If
a 10 g of carbon sample from a living tree gives
a rate of decay of 500 per hour whereas a 10 g
carbon sample obtained from an antique gives
a rate of decay of 100 per hour, determine the
age of the antique.

60

Solution 9.2.8: A  Aoet

Given T1  5 600 years A  eλt
Ao
2
Ao  eλt
A0 = 500 per hour A
A = 100 per hour
ln  Ao   t
  ln 2  A 

T1  ln Ao
A
2 t

  ln 2 year-1
t  ln ( )500 years
5600
100
  1.24 104 year-1
1.24 104

t  1.3104 years

61

Exercise 9.2:

4. Find the half-life of radioactive sample if its activity
decreased to 1/8 of its initial value in 9 days. (9 days)

5. The half-life of Radon 219 Rn is 4.0 s.
86
a) What do the numbers 86 and 219 represent in the symbol
Rn?
219 Rn.
86
b) Calculate the decay constant of 219
86
c) Given that 219 g of Radon contains 6.02  1023 atoms,
calculate the rate of disintegration of 1.00 g of Rn.
(0.173 s-1, 4.761021 Bq) 219
86

 6. of has a half-life of 78 minutes.
An isotope krypton 87 Kr
36
Calculate the activity of 10µg of krypton (in Bq and Ci).

(1.02  1013 Bq, 275.7 Ci)

62

7. A sample of radioactive material has an activity of 9.00 x
1012 Bq. The material has a half-life of 80.0 s. How long will
it take for the activity to fall to 2.00 x 1012 Bq ?

(174 s)

8. What mass of radium 227 would have an activity of 1.0 x
106 Bq? The half-life of radium 227 is 41 minutes.

(1.34  10-12 g)

9. (a) The half-life of the isotope 45K is 17.3 minutes. How long
will it take for 75% of the nuclei of the isotope to decay?

(34.6 min)

(b) After 4 hours, 80% of the initial number of nuclei of a
radioactive isotope have undergone decay. Calculate the
half-life. (1.72 h)

63

9.3 Particle Accelerator

At the end of this topic, the student should be able to : 64
a) State the thermionic emission.
b) Explain the acceleration of particle by electric and

magnetic field.
c) State the role of electric and magnetic field in

particle accelerators (LINAC and cyclotron) and
detectors (general principles of ionization and
deflection only).
d) State the need of high energies required to
investigate the structure of nucleon.

9.3 (a) THERMIONIC EMISSION

State that:

Process of emission of
charged particle (known
as thermion) from the
surface of heated metal.
(Gain enough kinetic
energy to leave the
surface when heated to a
very high temperature).
Charged particles
normally are
electrons.

65

**For additional knowledge  Electron orbiting the
nucleus at allow energy
level without emission of
e.m.radiation.

 When energy given to the
atom, electron will absorb
the energy and move to
the higher energy level
until far from the nucleus.

 This transition will emit
the e.m.radiation.

 If electron continue to
received the energy,
electron will be emitted
from atom.

 This process called as
‘Thermionic Emission’.

66

Number of electron emitted from the metal surface depends
on:
(i) Temperature
(ii) Surface area of metal
(iii) Work function of metal
**Different metal,
different work
function.

**For additional knowledge 67

Electron
Emitters

Television
Receivers

Electron Applications
Microscope of thermionic

emission

CRT Terminals

**For additional knowledge 68

9.3 (b) ACCELERATION OF PARTICLE
BY ELECTRIC & MAGNETIC FIELD

(i) Charged particle in uniform E

69

 Charged particle (electron),q enter perpendicularly with
uniform electric field, E.

 The E directed downward, so force acted on charged

particle directed upward.

=

=

∴ ………(1)
=

 If y is the transverse deflection during t,

= + 1 2 ………(2) , = 0 since q
2
enter horizontally

 Time taken to transverse the field, = ………(3)



70

 Combine equation (1), (2) & (3):

1 2
= 0 + 2

= 2 2
2

 When the q leave then E, vertical deflection occurred.
 Velocity of q increases in vertical direction.

= +


= 0 +

 So, energy of q also increases = 1 2
2
when v increases. 71

v parallel with E v perpendicular
(linear) with E

(parabolic)

 Electron is accelerated (magnitude of v ↑ )
 =

∴ = (constant).



 Electron moves towards positive plate.

72

(ii) Charged particle in uniform B

73

 Charged particle, +q enter perpendicularly with uniform
magnetic field, B.

 Charged particle deflected in the field without change

the velocity, v.

= Ԧ × ……..(1)
 perpendicular to v.

 Charged particle move along circular path in a uniform
magnetic field.

 So, the acceleration in circular path:

2
= ……..(2)

74

= ……..(3)

 Combine equation (1), (2) & (3):

2
=


∴ =
So, ∝

 The fast charged particles will move in large circle & the
slow ones move in small circle.

75

v perpendicular with E
(circular path)

 Electron is accelerated (direction changes)

 =

∴ = (constant).

 Electron moves in a circle.

76

(iii) Charged particle in uniform E & B
 If = &
 = 90°

=


∴ =

Therefore, charged
particles was
undeflected.

77

9.3 (c) ROLE OF ELECTRIC AND
MAGNETIC FIELD IN PARTICLE
ACCELERATORS & DETECTORS

What is the accelerator?

A device that uses electromagnetic field to propel
charged particles to high speed and to contain
them in well-defined beams.

Accelerator
at CERN

78

What is the detector?

A device used to indicate the presence of fast-moving
charged atomic or nuclear particles by observation of
the electrical disturbance created by particle as it
passes through the device known as radiation
detector.

79

LINAC (Linear Accelerator)

Role of combination E & B

 Used to accelerate the charged particle to high speeds.
 E: to accelerate charged particle and moves in straight

line (-ve to +ve) ↑.
 B: to maintain the charged particle to move at the

center of the pipe.

80

Circular Accelerator (Cyclotron)

Role of combination E & B

 Used to accelerate the
positively charged
particle to high speeds.
 E: to accelerate charged
particle from -ve to +ve
N plate ↑. (Imparts

charged particle energy
periodically)
 B: to bend the charged
particle in semicircle.
(Maintain charged
S particle in circular paths

81

Cyclotron

82

9.3 (d) THE NEED OF HIGH ENERGIES
REQUIRED TO INVESTIGATE THE
STRUCTURE OF NUCLEON

 The electrons surrounding a nucleus as a cloud. 83
 These electrons are negatively charged, so they

have a negative field that would repel other
negative things like other electrons.
 We need a certain energy to punch through the
electron cloud.
 Beyond that it becomes an issue of resolution.
 For example, electron microscopes. They use
electrons rather than light, because the
wavelength of any light would be too large to
study things as small as we want to study.

Conclusion of needed high energy…..

 Diffraction of the particle depend on their
wavelength.
 More energetic particle, the shorter of the
wavelength and the finer detail can be
observed.
 In other words, when high energy applied,
particle will move with greater velocity and the
wavelength will be shorter.
 So, high energy needed to investigate the very
internal structure of a proton and neutron.
(E ↑ needed for charged particle to enter the
nucleon)
84

9.4 Fundamental Particle

At the end of this topic, the student should be able to :
a) Explain the standard quark-lepton model

particles (baryons, meson, leptons and
hadrons).
b) Explain the corresponding antiparticle for every
particle.

85

9.4 (a) STANDARD MODEL OF PARTICLES
(BARYONS, MESONS, LEPTONS &
PHOTONS)

3 main particles
Bosons classifications Fermions

Hadrons Leptons

(made up of quarks) (6 leptons)

Gauge Mesons Baryons
bosons
(pair of quark (3 quarks)
&

antiquark)

86

Baryons

proton neutron Mesons

lambda sigma

omega pion kaon
neutral eta

pion

87

 Bosons and Fermions are distinguish by spin
number:

-Bosons have 0 or integer spin
-Fermions have spin



 Mesons & Baryons (classes of Hadrons)
distinguish by their masses and spin.

 So, Mesons - have 0 or integer spin number.
Baryons - have or spin number.



 And Leptons have spin number.



**For additional knowledg88e

 Comparison about interaction (force):

-Hadrons have strong
(Mesons & Baryons) interaction (force).

-Leptons have weak
interaction (force).

**For additional knowledge89

The Standard Model of Particles
Fermions
(matter particles) Bosons
(force carriers)

90

Leptons

 They are elementary particles.
 6 leptons are:
(i) electron, −
(ii) muon, − Have charge -1
(iii) tau, −
(iv) electron neutrino,
(v) muon neutrino, No charge

(vi) tau neutrino,

 6 anti-leptons are:
(i) anti-electron, +
(ii) anti-muon, + Have charge +1
(iii) anti-tau, −
(iv) anti-electron neutrino, ഥ
(v) anti-muon neutrino, ഥ No charge

(vi) anti-tau neutrino, ഥ

91

Quarks

 They are elementary particles.
 Combination of quarks produced other particles.

 Carry electric charge (multiple of ).

 6 quarks are:  6 antiquarks are:
(i) up, u (i) anti-up, ഥ
(ii) down, d
(iii) charm, c (ii) anti-down, ഥ
(iii) anti-charm, ത
(iv) strange, s (iv) anti-strange, ത
(v) top, t (v) anti-top, ҧ
(vi) bottom, b (vi) anti-bottom, ഥ

 Each quark has an antiparticle (antiquark).

92

TABLE 11.2

93

Atomic Nuclei = Combinations of Quarks

Baryons = particles made of 3 quarks

proton charge 221
3 + 3 − 3 = +1

up quark down quark

neutron charge 211
3−3−3=0

Mesons = particles made of pair of quark-antiquark

up quark pion charge 21
3 + 3 = +1

down antiquark

94

9.4 (b) ANTIPARTICLE FOR EVERY
PARTICLE

Every type of matter particle there is a
corresponding antiparticle with the same mass
and the opposite charge.
For example:
 Positron is the antiparticle of the electron
 Antiproton is the antiparticle of the proton
 Anti-muon is the antiparticle of the muon
 Antineutron is the antiparticle of the neutron
 Anti-tau neutrino is the antiparticle of the tau

neutrino

95

Anti-up Anti-down
Anti-top Anti-bottom
Anti-strange Anti-charm

positron Anti-electron neutrino

Anti-muon Anti-muon neutrino

Anti-tau Anti-tau neutrino

96

Particle Antiparticle

Charge = -1 Charge = +1

Charge = + Charge = −


Charge = 0
Charge = 0
97

GOOD
LUCK
FOR
PSPM 2

98