EP025 Lecture 8

CHAPTER 8 : QUANTIZATION OF LIGHT

8.1 PLANCK’S QUANTUM THEORY
8.2 THE PFOTOELECTRIC EFFECT

INTRODUCTION

One of the discoveries in the
early part of 20th century was
‘quantum theory’.

This theory led to significant
changes in how we look at the
physical world, including how we
describe the nature of light :

IS LIGHT A WAVE OR A
PARTICLE? .

INTRODUCTION

INTRODUCTION

Isaac Newton believed that light
consists of particles called
‘corpuscules’.

Later, Christian Huygens put
forward his wave theory of light
which proved by double-slits
experiment demonstrated by
Thomas Young in 1801.

INTRODUCTION

However, the debate continued when various
phenomena, such as :

• the black body radiation
• the photoelectric effect
provided evidence for the particle behavior of light.

INTRODUCTION

Eventually, between 1900-
1930, a modern version of
mechanics called ‘quantum
mechanics’ was proposed.

It was highly successful in
explaining many unexplainable
phenomena before, such as
light (and other fast moving
objects) and microscopic
system (such as atomic
structure) .

INTRODUCTION

CHAPTER 8 : QUANTIZATION OF LIGHT

9.1 PLANCK’S QUANTUM THEORY

Classical physics theory failed to
provide the ideas necessary to find
an agreement between the
experimental results and their
theoretical explanation.

In order to find the solution to this
problem, in 1900s Max Planck
proposed the Planck’s Quantum
Theory : a new-radical theory
based on several assumptions :

9.1 PLANCK’S QUANTUM THEORY

Assumption 1 :
The total energy radiated by a
heated material only with specific
quantities.

n

where h = Planck’s constant
= 6.626 x10-34 Js

n = quantum number.

9.1 PLANCK’S QUANTUM THEORY

Assumption 2 :

Energy is not emitted or absorbed
in a continuous form but in
packages called ‘quanta’ which
have certain discrete number.

9.1 PLANCK’S QUANTUM THEORY

Assumption 3 :
The smallest possible amount of
energy :

is called a quantum of energy or
normally known as ‘photon’.

The SI unit for photon is Joule (J)
or eV with relationship :

1eV = 1.6x10-19J

9.1 PLANCK’S QUANTUM THEORY

Albert Einstein then extended
Planck’s concept of quantization to
other electromagnetic waves.

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QUESTION 1

Calculate the energy of a photon of red light of
wavelength 7.20x10-7 m. Give your answer in both J

and eV.

ANSWERS
2.76x10-19 J or 1.73 eV

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QUESTION 2

Calculate the number of photons per second emitted
by a sodium vapour lamp of power 100 W. The
wavelength of sodium light is 590 nm.

ANSWERS
2.97x1020 photons s-1

CHAPTER 8 : QUANTIZATION OF LIGHT

9.2 THE PHOTOELECTRIC EFFECT

Photoelectric effect is the emission of electrons from
a metal surface when irradiated with light or other
electromagnetic radiations.

9.2 THE PHOTOELECTRIC EFFECT

Free electrons in the metal
absorb energy from the
incident light to enable them to
escape from the metal surface.

The emitted electrons are often
called ‘photoelectrons’.

Electrons, which have collected
at the anode, form a current in
the circuit, which is called a
‘photoelectric current’.

9.2 THE PHOTOELECTRIC EFFECT

The emission of electrons from
the metal surface depends on two
factors :
• Energy of the light, E = hf.
• Work function of the metal, Wo.

Work function, Wo refers to
minimum energy needed to
release an electron from the atom
of the metal (depends on the
types of metal used).

9.2 THE PHOTOELECTRIC EFFECT

The unit for is Joule (J) or eV.

Case 1 :
If E < Wo, then none electron
emits from the metal surface.

Case 2 :
If E = Wo, then electrons release
from the metal surface but no
energy supplied for electrons to
move.

9.2 THE PHOTOELECTRIC EFFECT

Case 3 :
If E > Wo, then electrons
release from the metal surface
immediately and move to the
anode (current flows, Io even
no voltage is supplied, V = 0).

9.2 THE PHOTOELECTRIC EFFECT

Relationship between the light
energy and the work function :

where :
Kmax = maximum kinetic energy

possessed by an electron.
The above equation is known as
Einstein’s equation.

9.2 THE PHOTOELECTRIC EFFECT

As a conclusion, ‘photoelectrons’
aren’t emitted unless the
frequency of light is greater than
the so called ‘threshold
frequency’, ho which refers to the
minimum frequency value of the
incident light which would remove
electron from the metal surface.

Relationship :

9.2 THE PHOTOELECTRIC EFFECT

If a voltage is supplied across the
anode and cathode, more energy
is supplied to the electrons. Thus,
more electrons reach to the
anode. Consequently,
‘photoelectric current’ increases.

Im refers to the maximum value
of ‘photoelectric current’ since all
the electrons reach to the anode
even the voltage is increased.

9.2 THE PHOTOELECTRIC EFFECT

If the polarity of the voltage is
overturned, the ‘photoelectric
current’ reduces due to the
reduction of the number of
electrons reach to the anode.

The electrons are slowing down
since the kinetic energy
possessed by the electrons is
reduced by reversed electric
potential energy supplied by the
voltage.

9.2 THE PHOTOELECTRIC EFFECT

If there is no more photoelectron
reaches the anode, then :

‘Stopping voltage’, VS is the
minimum reverse voltage needed
to stop the motion of electrons.
Therefore, the Einstein’s equation
can also be written as :

9.2 THE PHOTOELECTRIC EFFECT

The photoelectric current (the
number of photoelectrons
emitted per second), is directly
proportional to the intensity of
the incident light.

The increase in the photoelectric
current is due to the increase in
the rate of the emission of the
photoelectron, not because the
photoelectrons are emitted with
greater speeds.

9.2 THE PHOTOELECTRIC EFFECT

9.2 THE PHOTOELECTRIC EFFECT

9.2 THE PHOTOELECTRIC EFFECT

9.2 THE PHOTOELECTRIC EFFECT

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QUESTION 3

Cesium has a work function of 1.80 eV. When light of
wavelength 400 nm falls on the cathode of a photocell of
area 1.20 cm2, only one out of every five photons
succeeded in ejecting an electron. The photoelectric
current is 0.25 A. Calculate :
(a) threshold frequency of cesium.
(b) rate of emission of photoelectrons from the cathode.
(c) intensity of the incident light.
(d) maximum kinetic energy of the photoelectrons.
(e) maximum speed of the photoelectrons.

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ANSWERS
(a) 4.34x1014 Hz,
(b) 1.56x1012 s-1
(c) 3.23x10-2 W m-2
(d) 1.31 eV
(e) 6.78x105 m s-1