1.

Photo electric effect

2. Black body radiation
3. Compton effect
4. Emission of line spectra

The most outstanding development in modern science was the conception of Quantum
Mechanics in 1925. This new approach was highly successful in explaining about the
behavior of atoms, molecules and nuclei.
 The energy of a incident photon is utilized in two ways

1. A part of energy is used to free the electron from the atom known as photoelectric work-
function (Wo).
2. Other part is used in providing kinetic energy to the emitted electron .  1 mv 2 
2 

1 2
h  Wo  mv
2

This is called Einstein’s photoelectric equation.

 h  Wo  KEmax
h  h o  KEmax
KEmax  h(  o )
If   ,o no photoelectric effect

hc
Wo  h o 
o
hc 12400 o
o   A
Wo Wo (eV )
 If V0 is the stopping potential, then

KEmax  h(  o )

eVo  h  h o
h h o
Vo  
e e
It is in form of y = mx + c . The graph with V0 on y-axis and ν on x-axis will be a straight
line with slope h/e
 Compton Effect
The Compton effect is the term used for an unusual result observed when X-rays are
scattered on some materials.

By classical theory, when an electromagnetic wave is scattered off atoms, the wavelength of
the scattered radiation is expected to be the same as the wavelength of the incident
radiation.

Contrary to this prediction of classical physics, observations show that when X-rays are
scattered off some materials, such as graphite, the scattered X-rays have different
wavelengths from the wavelength of the incident X-rays.

This classically unexplainable phenomenon was studied experimentally by Arthur H.

Compton and his collaborators, and Compton gave its explanation in 1923.
When a monochromatic beam of X-rays is scattered from a material then both the
wavelength of primary radiation (unmodified radiation) and the radiation of higher
wavelength (modified radiation) are found to be present in the scattered radiation.
Presence of modified radiation in scattered X-rays is called Compton effect.
From Theory of Relativity, total energy of the recoiled electron
with v ~ c is
E  mc2  K  moc 2 Mass energy relation given by Einstein

K  mc2  mo c 2 K is the kinetic energy of the recoiling electron

mo c 2
K  mo c 2

1 v c2 2

 1 
K  mo c 2   1
 1  v 2 c 2 
Similarly, momentum of recoiled electron is
𝑚0 𝑣
𝑚𝑣 =
𝑣2
1 − 2
𝑐
 Now from Energy Conversation
 1 
h  h ' mo c 2   1
 1  v 2 c 2 
(i)

From Momentum Conversation

ℎ𝜈 ℎ𝜈 ′ 𝑚0 𝑣 along x-axis
= 𝐶𝑜𝑠𝜃 + 𝐶𝑜𝑠𝜙 (ii)
𝑐 𝑐 𝑣2
1 − 2
𝑐
and
ℎ𝜈 ′ 𝑚0 𝑣 (iii) along y-axis
0= 𝑆𝑖𝑛𝜃 − 𝑆𝑖𝑛𝜙
𝑐 𝑣2
1 − 2
𝑐
Rearranging (ii) and squaring both sides
 h h '
2

2 2
mv
  cos   cos2

o
(iv)
 c  1 v c
2 2
c
Rearranging (iii) and squaring both sides
 h '
2

2 2
mv
 sin    o
sin 2
 (v)
 c  1 v c
2 2

Adding (iv) and (v)

  
2 2
   
2 2 2
h h ' 2 h ' m ov
     cos 
 c   c  c 2
1  v 2
c 2

(vi)
 c c
But  and  ' So,
 '
1 1 h
mo c    (1  cos )
   '   '
  '  h
mo c  (1  cos )
  '   '
h
 '    (1  cos )
mo c
 is the Compton Shift.
It neither depends on the incident wavelength nor on the
scattering material. It only on the scattering angle i.e. 
h is called the Compton wavelength of the electron
mo c and its value is 0.0243 Å.
Experimental Verification

photon Bragg’s X-ray

Monochromatic Spectrometer
X-ray Source
θ

Graphite
target

1. One peak is found at same

position. This is unmodified radiation
2. Other peak is found at higher
wavelength. This is modified signal of
low energy. 
3.  increases with increase in  .
 Compton effect can’t observed in Visible Light

h
  (1  cos )  0.0243 (1- cosθ) Å
mo c
 is maximum when (1- cosθ) is maximum i.e. 2.
max  0.05 Å
So Compton effect can be observed only for radiation having
wavelength of few Å.

For   1Å  ~ 1%
For   5000Å  ~ 0.001% (undetectable)
 Pair Production
When a photon (electromagnetic energy) of sufficient energy passes near the field
of nucleus, it materializes into an electron and positron
This phenomenon is known as pair production.
Charge, energy and momentum remains conserved prior and after the production of pair.
The rest mass energy of an electron or
positron is 0.51 MeV (according to E = mc2).
The minimum energy required for pair
production is 1.02 MeV.
Any additional photon energy becomes the
kinetic energy of the electron and positron

The corresponding maximum photon wavelength is 1.2 pm. Electromagnetic waves with such
wavelengths are called gamma rays .
 Pair production cannot occur in empty space

From conservation of energy

h  2moc  2

here mo is the rest mass and

  1 1 v c 2 2

In the direction of motion of the photon, the

momentum is conserved if
h
 2 p cos
c
h  2cp cos
Momentum of electron and positron is

p  mo v

Equation (i) now becomes

h  2mo cv cos

v
h  2mo c    cos
2

c
But v  1 and cos  1
c
h  2moc 2
But conservation of energy requires that

h  2moc 2

Hence it is impossible for pair production to conserve both the energy and momentum
unless some other object is involved in the process to carry away part of the initial photon
momentum.

Therefore pair production cannot occur in empty space.

 Wave Particle Duality

Light exhibit both kind of nature: waves and particles