Basic Atomic and Nuclear Physics

1. Medical Physics
Phys 101
DR. SYED ISMAIL AHMAD. PhD
Asst. Prof. of Physics

2. Electromagnetic wave / spectrum

3. Photon, the quanta of Light
Quantum physics -the study of the microscopic world, where
the quantities are quantized.
The elementary amount that is associated with such a quantity
is called the quantum of that quantity (quanta is the plural).(
U.S. currency is quantized)
3
In 1905, Einstein proposed that electromagnetic
radiation (or simply light) is quantized and exists in
elementary amounts (quanta) called photons. Light
is an electromagnetic wave with a wavelength λ, a
frequency f, and a speed c (3x108 m/s) such that
Page # 272

4. According to Einstein, the quantum of a
light wave of frequency f has the energy
‘E’
Where h is the Planck constant,
h= 6.63 x 10-34 J.s
The smallest amount of energy a light wave of
frequency f is ‘hf, the energy of a single
photon.
4Page # 272

5. When light of frequency f is emitted or
absorbed by an atom, an amount of
energy ‘hf ’ is transferred from the atom
to the light or from light to atom.
, we can have photon
absorption and photon emission by
atoms in an object.
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Page # 272

6. Photoelectric effect
“When photons (Light)
of sufficient
frequency ‘f ’ (energy
hf ) incident on metal
surface, they collide
with valance ēs on
metal & give its
energy to it, then ēs
will be liberated from
the metal surface” .
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7. The Photoelectric Effect: If you direct a
beam of light of short enough wavelength
onto a clean metal surface, the light will
cause electrons to leave that surface (the
light will eject the electrons from the
surface). This is called ‘photoelectric
effect’
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Page # 274

8. Photoelectric Effect
The incident light shines on
target T, ejecting
electrons, which are
collected by collector cup
C. The electrons move in
the circuit in a direction
opposite the conventional
current arrows.
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Page # 274

9. Photoelectric equation:
Where Φ is work function. It is the
minimum amount of energy required to
eject ē from metal surface. Kmax is
maximum KE of emitted ē.
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If the electron is to escape from the target, it
must pick up energy at least equal to Φ. Any
additional energy (hf − Φ) that the electron
acquires from the photon appears as kinetic
energy K of the electron.
Page # 275

10. de-Broglie hypothesis – Matter Waves
According to de-Broglie a moving object (or)
particle has dual nature, both particle nature
and wave nature.
An object of mass ‘m’ moving with
velocity ‘v’ has wavelength associated it
is
“The waves associated with a material
particle are called matter waves”. They are
not E M waves.
10Mass – ‘m’ and
Kinetic energy ‘E’

11. 11
Problem: Find the de-Broglie wavelength of an
proton (mass m= 1.67x10-27 kg) moving with a
velocity 1.3x106 m/s ? (Take Planck’s constant
h= 6.63x10-34 Js)
Solution: Given mass m = 1.67x10-27 kg
Velocity v = 1.3x106 m/s
De-Broglie wavelength λ = ?
Formula h
m v
 =

34
27 6
6.63 10
1.67 10 1.3 10 /
Js
kg m s

−
−

=
  
13
3.05 10 m −
= 

12. Rutherford's model of the atom
The atom consists of mostly empty space, with a
very small, dense nucleus at centre where all of the
positive charge and most of the mass is contained.
Electrons resided in the empty space and revolve
around the nucleus in circular orbits. Introduction

13. Neutrons and protons are collectively called
nucleons. The different nuclei are referred to
as nuclides.
Number of protons: atomic number, Z
Number of nucleons: atomic mass number, A
Neutron number: N = A – Z
A and Z are sufficient to specify a nuclide. Nuclides
are symbolized as follows: .
13
The atom consists of a central
positive nucleus in which
electrons revolve around it
Pag 293

14. Isotopes :
Nuclei with the same atomic number, Z ,
but different neutron number, N are called
isotopes. (so they are the same element)
EX i): 79Au173 , 79Au197, 79Au204, 79Au207
EX ii)6C12,
6C13, 6C14
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Page #293
The light nuclides with N = Z are stable , i.e.
N/Z = 1

15. 15
Nuclear Radii and Atomic Mass
Nucleus of most atoms are considered as
spherical. Because of wave-particle duality,
the size of the nucleus is somewhat fuzzy.
Measurements of high-energy electron
scattering yield the radius ‘r’ as: r = ro (A1/3)
Problem: What is the radius of nucleus of Copper, 64Cu29 .
Solution: Given Copper, 64Cu29
Number nucleons , i.e. mass number A= 64
Size of nucleus formula
Page #295
1
15 3
(1.2 10 )( )r m A−
= 
1
15 3
(1.2 10 ) (64)r m−
=  
15
4.8 10r m−
= 

16. 16
Atomic Mass: Masses of atoms are
measured with reference to the carbon-
12 atom, which is assigned a mass of
exactly 12u where ‘u’ is a unified atomic
mass unit. 1u = 1.66x10-27 kg
Mass excess (Δ): Δ = M - A , where M is
actual mass of atom in u and A is mass
number

17. Nuclear Binding Energy
The total mass ‘M’ of a nucleus is always less
than the sum of the masses (Σm) of its
separate protons and neutrons. Mass Defect,
Δ = Σm - M , Where has the mass gone?
It has become energy (E= mc2 ) [c=3x108 m/s]
Mass energy of nucleus Mc2 < total mass
energy Σmc2
This difference between these two energies is
called the total binding energy Ebe of the
nucleus.
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Page #296
Mass Defect = Sum of masses of nucleons – mass of nucleus

18. Binding energy per nucleon of a nucleus is
defined as ratio of binding energy ( ) of
nucleus to number of nucleons (A) in the
nucleus.
A greater binding energy per nucleon means more
tightly bound nucleus i.e. more stable nuclides have
higher BE/A than the less stable ones.
Page #296
Large nuclei
– Loosely
bound
Tightly bound
Small nuclei -
Loosely bound

19. Fe, Ni has highest binding energy per nucleon, so
more stable.
Extreme RHS nuclei are more tightly bound
compared to extreme LHS (lower side)
Page # 296

20. Nuclear fusion:
When two or more nuclei combine to form a
single nucleus (new element) with a
higher atomic number (more protons in the
nucleus). [Occurs in stars and sun]
Nuclear Fission: When a heavy a nucleus (ex-
U, Pu) splits into photons in the form of
gamma rays and other subatomic particles
that releases free neutrons and lighter nuclei
is called Nuclear Fission.
Page # 297

21. Radioactivity: Too many or too few neutrons
will make the nucleus unstable & decay,
giving out energy and /or ionizing radiations
alpha (α), beta (β), and gamma (γ) in a random
process (‫عشوائية‬ ‫.)عملية‬ This decay phenomenon
is called “Radioactivity” which is a
spontaneous process(‫عفوية‬ ‫)عملية‬
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Page # 299
Radioactive Decay
Alpha and beta rays are
bent in opposite
directions in a magnetic
field, while gamma rays
are not bent at all.

22. 22
Radioactivity was discovered by Henry Becquerel
and coined by Marie Curie.
2 protons + 2 neutrons= α Particle
Page # 299

23. Radioactive Decay and Half-Life
Nuclear decay is a random process (we
cannot predict); the decay of any nucleus is
not influenced by the decay of any other.
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dN
R = - .
dt Page #
299/300
The number of atoms decaying per unit time
(-dN/dt) is called activity ‘R’

24. The activity of a radioactive sample is the rate
at which atoms decay.
If a sample contains N radioactive nuclei, then
the rate of decay ‘R’ ( ) is proportional to
N , therefore
The proportionality constant ‘’ is called
‘disintegration constant’ or ‘decay constant’
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Mathematically we can show that
dN
R = - .
dt
Each radioactive nuclide
has a different decay
constant, 
R = N
Page # 300

25. The total decay rate ‘R’ of one or more
nuclides is called ‘activity’ SI unit ‘becquerel’
1 becquerel = 1 Bq = 1 decay event/second.
Another unit of activity is the curie (Ci)
1 curie = 1 Ci = 3.70x1010 events/s =
3.70x1010 Bq . Another unit is Rutherford.
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Experimental measurements show that the
activities of radioactive samples fall off
exponentially with time.
-λt
0R = -R e .
Page # 300

26. 26
( )
1/2 1/2
ln 2 0.693
= =
Τ Τ

Half-Life (T1/2): The time required for the number of
radioactive atoms in a sample to decrease by one
half

27. Half-Life: The half-life, T½, is the time it takes for the
activity to drop by ½. We can find a relationship
between  and T½: Using
original activityactivity after T½
1/2-λΤ1
= e
2
1/2+λΤ
e =2
( )1/2Τ =ln 2
( )
1/2 1/2
ln 2 0.693
= =
Τ Τ

Page # 301
Problem: The half-life
a material is 30 years.
What is its
disintegration
constant?
Ans: 7.32 x10-10 s-1

28. (i) The half-life of a radioactive isotope is
the time taken for half of the nuclei in a
sample of the radioactive isotope to
decay.
(ii) The fraction of undecayed nuclei left
(remained) after n half-lives is 1/2n.
N/ N0 = ( 1/2)n
(iii) The relationship between decay
constant,λ, and half-life,T1/2 , is given
by:T1/2 = 0.693/ λ

29. Problem: The half-life a material is 30 years.
What is its disintegration constant?
Ans: λ= 7.32 x10-10 s-1
Solution: Given- Half-Life
1
2
30 30 365 24 60 60T years= =    
6
946080000 946.08 10 s= = 
1
12
2
0.693 0.693
:Rule T
T


= → =
6
0.693
946.08 10
 =

1
2
30T years=

30. Example: radon has a half-life of 3.8
days. If you start with 1 mg of radon,
after 3.8 days you will have 0.5 mg of
radon. Days Radon Left (mg)
0 1
3.8 days (1T1/2) 0.5
7.6 days (2T1/2) 0.25
11.4 days (3T1/2) 0.125
15.2 days (4T1/2) 0.0625
The fraction of undecayed nuclei left after n half-
lives is 1/2n → N/N0 = 1/2n
t = n x T1/2

31. Alpha Decay (α- particles decay)
An alpha (α) particle consist of 2 protons & 2
neutrons. It is a helium, 4He2 nucleus.
i) It is +vely charged particle, its mass is higher
or greater than that of β & γ particles, but has
least penetration power.
ii) When an element disintegrates by emitting α
particle its atomic number ‘Z’ decreases by 2
units and mass number ‘A’ by 4 units.
• Ex: If 238U92 emits an α particle , then it is
converted in to 234Th90
238U92
234Th90 + 4He2 (α - particle)
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Page # 302

32. Rn
222
86
He
4
2
+Po
218
84
He
4
2
208Po84
→ 204Pb82+ 4He2 (α -particle)
He
4
2
+Ra
226
88
He
4
2
Th
230
90
Page # 302

33. 238U92---------> 234Th90 + 4He2 (α - particle)
The mass energy of the decay products
234Th and 4He is less than original 238U.
The difference of mass -∆M is converted
in to energy, called ‘Q’ value Q = -∆Mc2
The mass energy is also called Decay’s
disintegration energy Q
4.25 MeV energy is released in the above reaction
Page #302

34. ➢Beta decay occurs spontaneously due to
internal conversion of proton and neutrons in
the nucleus by emitting an electron or a
positron.
➢Charge and nucleon number remain conserved.
➢Beta minus decay
➢Beta plus decay
ν is called neutrino, a neutral particle with
negligible mass, which interact weakly with
matter.
Beta Decay
Page # 305

35. When a nucleus emit a β minus particle
its atomic number increases by 1 unit,
but mass number remain same.
For a Beta minus decay (β-) decay
For a Beta plus decay (β+) decay
In Beta decay, one type of nucleon converts in to
other type, so no change in nucleon number
Page # 306

36. Problem: How many α (2He4)particles and -1β0
(minus, -1e0) particles are emitted when 92U238
decays to 82Pb206 ?
92U238 _______> 8α + 6β + 82Pb206

37. α- particles are massive & +ve charged have low
penetration depth and high ionizing power.
β particles are like fast moving ēs , less massive
than α- particles and have medium penetration and
ionizing power.
γ particles are E M radiation, Photons having no
mass &charge. They are very fast so have strong
penetration but weak ionizing power.
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