Nuclear physics describes the structure and interactions of atomic nuclei. Rutherford discovered the nucleus through alpha scattering experiments. Protons and neutrons were later identified. Isotopes have the same number of protons but different numbers of neutrons. Mass defect and binding energy explain why atomic nuclei are more stable than separated nucleons. Radioactive decay occurs spontaneously at a rate proportional to the number of unstable nuclei. Exponential decay and half-life are described by the decay constant. Nuclear reactions conserve nucleon number and charge. Energy is released or absorbed through mass-energy equivalence. Fission and fusion occur under different conditions according to binding energy. Controlled fission in reactors uses moderation and feedback to sustain a chain reaction. Fusion

1. 25.0 Nuclear Physics
25.1 Nucleus
25.2 Radioactivity
25.3 Nuclear Reaction

2. LEARNING OUTCOME
(a) describe the discovery of protons and
neutrons (experimental details are not required);
(b) explain mass defect and binding energy;
(c) use the formula for mass-energy equivalence ;
(d) relate and use the units J and MeV;
(e) sketch and interpret a graph of binding energy
per nucleon against nucleon number;

3. Discovery of Protons and neutrons
Evidence for a nucleus

4. Rutherford’s explanation
• A neutral atom contains equal amounts of positive (+) and
negative (-) charge . The above experiment, supervised by
Ernest Rutherford , first provided evidence that an atom's
positive charge and virtually all of its mass is concentrated
in one small region of the atom.
•
• A thin piece of gold foil was bombarded with alpha
particles, which are positively charged. Most of the alpha
particles passed straight through the gold atoms, but a few
were repelled so strongly that they bounced back or were
deflected through large angles. These results led
Rutherford to propose this model of the atom: a heavy,
positively charged nucleus at the centre, with much lighter,
negatively charged electrons in orbit around it.

5. Atomic number and mass number
A
Z X

6. Isotopes
• Isotopes of an element have the same proton
number but different nucleon numbers. The
nucleon numbers differ because the nuclei
have different numbers of neutrons.
• They have the same electron arrangement
and, therefore, the same chemical properties

7. Mass defect and binding energy
• The unified atomic mass unit, a.m.u (u) is used
for measuring the masses of atomic particles.
It is very close to the mass of one proton (or
neutron). it is defined as follows:
• Converting into kg, 1 u = 1.66 x 10-27 kg.
1 u = mass of carbon-12 atom
12

8. Mass defect
• Rest Mass
Rest Mass is the mass of an atom at rest, when
measured by an observer who is at rest in the
same frame of reference. Rest mass of particle
given by:

9. Mass defect
Mass Defect m can be concluded as follows:
m=[Zmp+(A-Z)mn]-MN
mp = mass of proton
mn = mass of neutron
MN = mass of nucleus (composite mass of nuclide)
Mass defect is the mass different between composite
mass of nuclide nucleon and the sum of it nucleons.

10. Binding energy
• Einstein's theory of relativity is that energy has
mass.
• The change of energy E is linked to the change
of mass m(mass defect) by this equation:
unit : Joule(J)
m = in kg
m = (__ u x 1.66 x 10-27) kg
where c is the speed of light: 3 x 108 m s-1
2
E mc
 

11. Binding energy
• Binding energy is the nuclear energy required
to completely separate the nucleus of an atom
into its component (nucleons).
Binding Energy EB = (mass defect) x (c2)
= m c2
= [[Zmp+(A-Z)mn]-MN ] c2
Unit = Joule (J)

12. Binding energy
With nuclear particles, energy is often measured in MeV (the electron-volt :
eV)
1 MeV = 1.60 x 10-13 J
By converting 1 u into kg and applying E =mc2
1 u is equivalent to 931 MeV
Binding Energy EB = (mass defect in u) x 931 MeV
Binding Energy of Helium = 0.0304 x 931
= 28.3 MeV
= 28.3 x 106 (1.6 x 10-19) J
= 4.53 x 10-12 J
= 0.0304 x 1.66 x 10-27 x (3 x 108) 2 J
= 4.54 x 10-12 J

13. Binding energy per nucleon vs
nucleon number graph
The stability of a nucleus depends on
the binding energy per nucleon. The
graph above shows how this varies
with nucleon number. The line gives
the general trend; points for some
individual nuclides have also been
included.
Note:
• Nuclei near the 'hump' of the graph
are the most stable, because they need
most 'unbinding energy' per nucleon.
• A graph of mass defect against
nucleon number has the same general
form as the graph above.

14. 25.2 Radioactivity
Learning Outcome
(f) explain radioactive decay as a spontaneous and
random process;
(g) define radioactive activity;
(h) state and use the exponential law
for radioactive decay;
(i) define decay constant,;
(j) derive and use the formula
(k) define half-life, and derive the relation
(l) solve problems involving the applications of
radioisotopes as tracers in medical physics;
N
dt
dN



t
e
N
N 

 0
2
1
2
ln
t



15. Radioactive decay
• Radioactive decay is the random and
spontaneous process by which produce , and 
ray, and it is random and spontaneous.
• Random means that every atom have the same
probability to decay
• Spontaneous means that the process is
unpredictable. It is not depend on any physical
factor (temperature, mass etc)

16. Radioactive decay

17. Stability of the nucleus
If the number of neutrons
(A - Z) in the nucleus is
plotted against the number
of protons (Z) for all known
nuclides, the general form
of the graph is like this:

18. Radioactive Activity, A
The activity,A of a radioactive source is the
number of disintegrations occurring within it per
second.
The SI unit of activity is the Becquerel (Bq):
1 Becquerel = 1 disintegration s-1 (1 Bq = 1 s-1)
dN
A
dt
 

19. The radioactive decay’s law
Decay’s Law state that the rate of decay is directly proportional
to the decreasing of number of nuclei present.
Unstable nuclei disintegrate spontaneously and at random.
However, the more undecayed nuclei there are, the more
frequently disintegrations are likely to occur. For any radioactive
nuclide, on average.
The mathematical analysis of radioactive decay is based on two
simple assumptions:
a. Decay is completely random
b. The rate of decay is directly proportional to the number of
unstable nuclei,N present
dN
N
dt
 

20.  is called the radioactive decay constant.
 decay constant is defined as the probability of decay per unit
time
dN
N
dt
 
dN
N
dt

 
𝝀 =
𝒅𝑵
𝑵
𝒅𝒕
𝑨 = −𝝀𝑵

21. Derive
dN
N
dt

 
1
𝑁
𝑑𝑁 = −𝜆 𝑑𝑡
ln 𝑁 𝑁𝑜
𝑁
= −𝜆 𝑡 0
𝑡
0
t
N N e 



22. Half Life, 𝒕𝟏
𝟐
time taken for
the number
of undecayed
nuclei to
halve in value

23. 0
2
N
N 
0
t
N N e 


1
2
0.693 ln2
t
 
 
0
1
2
n n
A A

dN
A
dt
 

24. Use of radioisotopes
i) Tracers-their movements can be tracked. Examples include:
•tracking a plant's uptake of fertilizer from roots to leaves by adding a
tracer to the soil water,
•detecting leaks in underground pipes by adding a tracer to the fluid in
the pipe.
ii) Testing for cracks  rays have the same properties as short-
wavelength X-rays, so they can be used to photograph metals to reveal
cracks. A  source is compact and does not need an electrical power
source like an X-ray tube.
iii) Cancer treatment  rays can penetrate deep into the body and kill
living cells. So a highly concentrated beam from a cobalt-60 source can
be used to kill cancer cells in a tumour. Treatment like this is called
radiotherapy.

25. Use of radioisotopes
iv) Carbon dating Living organisms are partly made from carbon which
is recycled through their bodies and the atmosphere as they obtain
food and respire. A tiny proportion is radioactive carbon-14 (half-life
5730 years). This is continually forming in the upper atmosphere as
nitrogen-14 is bombarded by cosmic radiation. When an organism
dies, no new carbon is taken in, so the proportion of carbon-14 is
gradually reduced by radioactive decay. By measuring the activity, the
age of the remains can be estimated to within 100 years. This method
can be used to date organic materials such as wood and cloth.
v) Smoke detectors These contain a tiny a source which ionizes the air
in a small chamber so that it conducts a current. Smoke particles
entering the chamber attract ions and reduce the current. This is
sensed by a circuit which triggers the alarm.

26. Nuclear Reaction
Learning Outcome:
(m) state and apply the conservation of nucleon number and
charge in nuclear reactions;
(n) apply the principle of mass-energy conservation to
calculate the energy released (Q - value) in a nuclear reaction;
(o) relate the occurrence of fission and fusion to the graph of
binding energy per nucleon against nucleon number;
(p) explain the conditions for a chain reaction to occur;
(q) describe a controlled fission process in a reactor;
(r) describe a nuclear fusion process which occurs in the Sun.
https://www.meta-synthesis.com/webbook/33_segre/segre2.html
https://atom.kaeri.re.kr/nuchart/?zlv=2

27. Nuclear Reaction
In nuclear physics, a nuclear reaction is a
process in which two nuclei or nuclear particles
collide, to produce different element of nuclei.
• charge and total number of nucleons are
conserved
• Energy is conserved in a nuclear reaction
The energy comes from the reaction equivalent
of the decrease in mass in the reaction

28. The total mass after the reaction is less than the
total mass before the reaction. The difference in
mass is known as the mass defect of the
reaction.
Nuclear Mass defect,
m = (total mass before the reaction) - (total mass after the reaction)
Energy, Q released = (m)c2

29. Nuclear Fission
• Nuclear Fission is define as splitting of a large nucleus by
bombarding with neutron into two smaller nuclei which are almost
equal in size.
• Slow neutrons are more likely to initiate a nuclear reaction as they
are more easily captured by the nucleus.

30. A heavy nucleus
undergoes fission,
the product nuclei
have smaller
nucleon numbers
and higher binding
energy per nucleon

31. Chain Reaction
• In the fission of uranium-235 nucleus,
two or three secondary neutrons are
produced. These secondary neutrons
can cause the fission of other uranium-
235 nuclei.
• A chain reaction occurs when the
secondary neutrons from subsequent
fission of uranium-235 nuclei continue
the fission reaction.
To maintain a chain reaction, a minimum of one neutron from each
fission must cause further fission. However, to achieve this, these
problems must be overcome:
• The fission of uranium-235 produces medium-speed neutrons. But
slow neutrons are better at causing fission.
• Less than 1 % of natural uranium is uranium-235. Over 99% is
uranium-235, which absorbs medium-speed neutrons without fission
taking place.

32. Nuclear Reactor
• Moderator : Water is now used as moderator to slow down the
neutrons. Earlier models of nuclear reactors used graphite as moderator.
• Control rods : Control rods of boron or cadmium are used to absorb
the secondary neutrons so that only one of the secondary neutrons
from the fission of a uranium-225 nucleus is allowed to continue the
chain reaction.
• Coolant : Water circulating in the core of the reactor acts as coolant.
The hot water flows to the heat exchanger where steam is produced.
The steam produced under high pressure rotates the turbines of the
generator to generate electricity.
The main features of the nuclear
reactor are
• Fuel: The fuel is enriched
uranium-235 which has been
enriched from 0.7% to 3% or 4%
so that the chain reaction can be
self-sustaining.

34. Nuclear Fusion
• Nuclear fusion is the process of combining two small
nuclei to form a larger nucleus.
• The mass of the product nucleus is less than the total
combined mass of the two light nuclei.
• The energy equivalent of the difference in mass is
released as energy.
m = (total mass before the reaction) - (total mass after the reaction)
Energy, Q released = (m)c2

35. Nuclear Fusion
• The nuclei must have sufficient kinetic energy
to overcome the repulsive Coulomb force
between themselves.
• Temperature is increased to an extremely high
value of the order of 108 K. Collisions of the
high-energy deuterium nuclei produce fusion.
• The Sun generates an estimated power of 4 x
1020 W and transforms 50 trillion tonnes of
hydrogen into helium per day.