As per syllabus of Gondwana University Gadchiroli

1. Unit -III
Nuclear Reactions and Interaction of
nuclear radiation with Matter

2. Nuclear Reaction
• When a target nucleus is bombarded with fast
moving particles , the resulting interaction ,in
which the identity or characteristics of
incident particles are changed is known as
nuclear reaction.
• The simple nuclear reaction can be written as
a + X → Y + b
Incident target product product
Particle Nucleus Nucleus particle

3. • The first nuclear reaction was studied by
Rutherfort in 1919 . He bombarded nitrogen
nuclei i.e. target with 𝛼 – particles and
showed that protons were given out
• 7
14
𝑁 + 2
4
𝐻𝑒 → 8
17
𝑂 + 1
1
𝐻 + Energy

4. Types of nuclear reaction
• Elastic scattering- in this case , the incident
particle strikes the target nucleus and leaves
without loss of energy , but with altered
direction of motion . In an elastic scattering ,
target nucleus remains unaffected
Ex-The large angle scattering of 𝛼 – particles
from thin gold foil .
2
4
𝐻𝑒 + 79
197
𝐴𝑢 → 79
197
𝐴𝑢+ 2
4
𝐻𝑒

5. • Inelastic scattering- In this case , the kinetic
energy is not conserved . But a part of energy
of incident particle is taken up by the target
nucleus which is excited to a higher quantum
state, later on it decay to ground state
radiating the excess energy in the form of 𝛾 –
radiation.

6. • Radiative Capture-in this case , the incident
particle is captured by the target nucleus and
a new nucleus is formed . In general , the new
nucleus has a considerable excess of energy
and decays with the emission of one or more
𝛾 – ray photons.
• Disintegration- In this type of reaction , the
incident particle is absorbed by the target
nucleus and a different type of particles are
emitted . The composition of the resultant
nucleus is also different from the parent
nucleus .

7. Conservation laws
• Conservation of mass numbers-
The total mass number or total number of
nucleons before and after the reaction remains
the same.
• Conservation of charges-
The total charge before and after the reaction
must be conserved.

8. • Conservation of mass and energy-
The total mass – energy in a nuclear reaction
remain unchanged. It means that in a nuclear
reaction , neither kinetic energy nor rest mass is
conserved by itself but their total is always
conserved.
• Conservation of linear momentum-
The total linear momentum of the particles
taking part in a nuclear reaction must be same
before and after nuclear reaction.

9. Q- Value of Nuclear Reaction
• The total energy released or absorbed in the
nuclear reaction.
• It is equal to change in total kinetic energy of
the system. It may be positive or negative

10. • Consider the nuclear reaction .
a + X → Y + b
• In this nuclear reaction , the fast moving particle ‘
a ‘ with kinetic energy 𝐸𝑎 is incident on the
target nucleus X , which is assumed to be rest.
• The outcome of the nuclear reaction is the
product nucleus Y having Kinetic energy 𝐸𝑦 and a
new emitted particle ‘b’ with kinetic energy
energy 𝐸𝑏.
• The total change in kinetic energy i.e. Q – value is
given by
Q = (𝐸𝑦 + 𝐸𝑏 ) - 𝐸𝑎 ---------(1)

11. • Let 𝑀𝑥 and 𝑀𝑦 be the rest mass of target nucleus
and product nucleus.
• And 𝑚𝑎and 𝑚𝑏 be the mass of incident and
emitted particle.
• According to law of mass-energy conservation
𝑀𝑥𝑐2
+ (𝑚𝑎𝑐2
+ 𝐸𝑎) = (𝑚𝑦𝑐2
+ 𝐸𝑦) + (𝑚𝑏𝑐2
+ 𝐸𝑏)
(𝐸𝑦 + 𝐸𝑏 ) - 𝐸𝑎 = (𝑀𝑥 + 𝑚𝑎) 𝑐2
- (𝑀𝑦 + 𝑚𝑏) 𝑐2
Q = (𝑀𝑥 + 𝑚𝑎) 𝑐2
- (𝑀𝑦 + 𝑚𝑏) 𝑐2
Hence the Q value of a nuclear reaction is defined
as the difference between kinetic energies of
product and incident particle.

12. • Exo-ergic nuclear reaction –
If the Q- value of a nuclear reaction is positive
then there is liberation of energy and it is known
as axoergic ( exothermic ) nuclear reaction.
In this case , the K.E. of products is greater
than the K.E. of reactants and the energy is
released in the process.
(𝐸𝑦 + 𝐸𝑏 ) > 𝐸𝑎
Hence Q >0 , The reaction is axoergic

13. Endo-ergic nuclear reaction
If the Q- value of a nuclear reaction is negative
then there is absortion of energy and it is known
as endoergic ( endothermic ) nuclear reaction.
In this case , the K.E. of products is less
than the K.E. of reactants and the energy is
released in the process. Energy is required for
the reaction
(𝐸𝑦 + 𝐸𝑏 ) < 𝐸𝑎, Hence Q <0 , The reaction is
endoergic

14. Nuclear reaction cross-section
• The probability of occurrence of a nuclear
reaction is expressed in terms of cross-section
of a nuclear reaction.
• It is defined as the effective target area
presented by the nucleus to the incident
particle for a particular type of nuclear
reaction .
• It is denoted by 𝜎

15. • Consider the slab of material whose area is ‘A ‘
• Thickness dx
• Volume of the slab A.dx
• Let n be the atom per unit volume in the
target material.
• Total number of nuclei in the slab = nAdx
• We assume that each nucleus has cross-
section of 𝜎.
• Aggregate cross-section for all nuclei= 𝜎nAdx

16. • Let N = number of incident particle in a
bombarding beam.
• dN = number of particle that interact with
nuclei in the slab.
•
𝑑𝑁
𝑁
=
𝐴𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒 𝑐𝑟𝑜𝑠𝑠−𝑠𝑒𝑐𝑡𝑖𝑜𝑛
𝑡𝑎𝑟𝑔𝑒𝑡 𝑎𝑟𝑒𝑎
=
𝜎nAdx
𝐴
= 𝜎ndx
• 𝜎 =
𝑑𝑁/𝑁
𝑛𝑑𝑥
---------(1)
• This is the expression for microscopic cross-
section per nucleus

17. Cerenkov Radiation
• It has been observed that when a high energy
charge particle with nonzero rest mass such as
electron, travels faster than the speed of light in
the medium, then the particles emits special kind
of radiation called Cerenkov radiation.
• The wavelength of Cerenkov radiation lie in and
around the visible region of electromagnetic
spectrum.
• The characteristics blue glow of an under water
reactor is due to Cerenkov radiation .

18. • Cerenkov radiation is emitted in the form of a
cone having an angle 𝜃 defined by
cos 𝜃 =
1
𝛽𝑛
, Here 𝛽 =
𝑣
𝑐
Where
n = refractive index of the medium.
v = velocity of particle in the medium.
c = velocity of light in vacuum.
the necessary condition for the emission of
Cerenkov radiation is
𝛽 >
1
𝑛
but 𝛽 =
𝑣
𝑐
,hence v >
𝑐
𝑛

19. • Here
𝑐
𝑛
is velocity of light in the medium.
• Cerenkov radiation is an electromagnetic
radiation , emitted by an energetic charged
particle travelling through a dialectic medium
at a speed faster than that of light in that
medium.

20. Absorption of 𝛾 – rays by matter
• The 𝛾 rays are electromagnetic radiations
consisting of a stream of very high energy
photons.
• When a beam of 𝛾 – ray photons is made to
incident on the sheet of absorbing material ,
each photon is removed individually from the
beam in a single event.
• This process is responsible for the absorption
of 𝛾 rays in the matter .

21. • The emergent beam from the absorbing sheet
is found to have a smaller intensity i.e. it is
said to be attenuated.