State and explain Alpha , Beta and Gamma decay

State and explain 𝛼 , 𝛽 and 𝛾 decay
SYEDA NIMRA SALAMAT

𝛼-decay
1. Why there is a need of alpha decay?
2. History
3. State alpha decay + Generalized equation
4. Explanation of alpha decay
5. Gamow’s theory of alpha decay + Geiger
Nuttall law
6. Diagram + Table + Graph
7. Examples
8. Summary
Syeda Nimra Salamat 2/16/2021

Why there is a need of 𝛼-decay?
Alpha decay occurs most often in massive
nuclei that have too large a proton to neutron
ratio. Alpha radiation reduces the ratio of
protons to neutrons in the parent nucleus,
bringing it to a more stable configuration.
Many nuclei more massive than lead decay by
this method.

History:
Alpha particles were first described in the investigations of
radioactivity by Ernest Rutherford in 1899, and by 1907 they were
identified as He2+ ions. By 1928, George Gamow had solved the
theory of alpha decay via tunnelling.

State 𝛼-decay + Generalized equation:
‘A radioactive process in which a parent nuclei decay into
daughter nuclei and alpha particle with some energy
liberated.’
It is denoted by 𝛼 𝑜𝑟 𝐻𝑒2+ , 𝛼2+.
𝐙
𝐀
𝐗 → 𝐙−𝟐
𝐀−𝟒
𝐘 + 𝟐
𝟒
𝜶
 𝒁
𝑨
𝑿 is the parent nucleus
 A is the total number of nucleons
 Z is the total number of protons
 𝒁−𝟐
𝑨−𝟒
𝒀 is the daughter nucleus
 𝟐
𝟒
𝜶 is the released alpha particle

Explanation of 𝛼 –decay:
 When an alpha particle are ejected from nucleus its
mass number is reduced by four and atomic number
reduced by two. This is occur to increase the stability of
the nucleus.
 Alpha decay is a barrier penetration process.
 Imagine an alpha particle bounded by nuclear force
and once it get out from the Nucleus it feels coulomb
repulsive force.
 By using Gamow's theory of beta decay and
Geiger Nuttal law.

Gamow’s Theory Of 𝛼-Decay:
I. In different kind of alpha decay the
maximum kinetic energy of the alpha
particle is about 4-9MeV. While the energy
of barrier penetration is of about 25MeV.
II. The question here arises that how the
alpha particle overcome such a large force
and escape out. For this question Gamow
introduces Gamow's theory of alpha
particle.
III. It is impossible to explain classically
therefore we solve it quantum
mechanically.
IV. He borrowed quantum tunnelling concept
to explain this problem.

Quantum tunnelling:
Here particle shows wave mechanical
behaviour. It makes continuous strikes to
overcome the barrier and penetrate through
it.
The transition probability of escape particle
is given as;
𝑻. 𝑷 = 𝒆−𝟐𝒌𝟐𝑳 𝒌𝟐 =
𝟐𝒎(𝑽−𝑬)
ℏ

Gamow’s Theory Of 𝛼-Decay :
• We use two different elements to compare alpha
particles of different kinetic energies.
𝐄𝟐 > 𝐄𝟏
• L is the width of barrier if width increase the
transition probability decreases.
𝐖 ↑ 𝐓. 𝐏. ↑
• 𝑻. 𝑷. 𝑬𝟐 > 𝑻. 𝑷. (𝑬𝟏)
• The half life of high energy particle is less than
low energy particle.
• 𝑻𝟏
𝟐
(𝑬𝟐) < 𝑻𝟏
𝟐
(𝑬𝟏)
• For high energy –particle
𝑳 ↓ 𝑻. 𝑷. ↑
For low energy –
particle
𝑳 ↑ 𝑻. 𝑷. ↓
L

Geiger Nuttall Law:
a. It is basically the experimental observation
Gamow's theory according to which;
b. Short lived alpha particles have high kinetic
energy while longer lived alpha particles
have lesser kinetic energy.
c. In this law the half life and kinetic energies of
large number of alpha particles were observed
undergoing decay process.
d. the graph plotted between half life and kinetic
energy is…
e. The formula relation derived is given;
f. 𝐥𝐨𝐠𝟏𝟎𝐓𝟏
𝟐
= 𝐙
𝐄
𝐚𝟏 + 𝐚𝟐
𝐙
𝐄
𝐥𝐨𝐠
𝟏𝟎
𝐓
𝟏
𝟐

Table:
Symbol Charge Mass
Ionization
energy
Nature of
radiation
Relative
penetrating
power
𝜶 2+ 𝟔. 𝟔 × 𝟏𝟎−𝟐𝟒
𝒈
Intermediat
e 𝒁
𝑨
𝑯 𝒏𝒖𝒄𝒍𝒆𝒊 1
Alpha decay

Examples:
 Alpha decay of radium-226 is;
𝟖𝟖
𝟐𝟐𝟔
𝑹𝒂 → 𝟖𝟔
𝟐𝟐𝟐
𝐑𝒏 + 𝟐
𝟒
𝐇𝐞
In this example an unstable atom is
converted into stable atom by emission of
an alpha particle.
 Alpha decay of radon gas into solid
polonium and through emitting an alpha
particle.
𝟖𝟔
𝟐𝟐𝟐
𝑹𝒂 → 𝟖𝟒
𝟐𝟏𝟖
𝑷𝒐 + 𝟐
𝟒
𝐇𝐞

Summary:
Alpha decay is one process that
unstable atoms can use to become
more stable. During alpha decay,
an atom's nucleus sheds two
protons and two neutrons in a
packet that scientists call
an alpha particle. Since an atom
loses two protons during alpha
decay, it changes from one element
to another.

𝜷-decay
2. History
3. State alpha decay + Generalized
equation
4. Explanation of alpha decay +
Neutrino Hypothesis
5. Diagram + Table + Graph
6. Examples
7. Summary

Why there is a need of 𝛽-decay?
Beta decay conserves a quantum number
known as the number of electrons and their
associated neutrinos. β+ decay also results in
nuclear transmutation, with the resulting
element having an atomic number that is
decreased by one.

History:
Beta decay was named (1899) by Ernest Rutherford when he observed
that radioactivity was not a simple phenomenon. He called the less
penetrating rays alpha and the more penetrating rays beta. Most beta
particles are ejected at speeds approaching that of light.

State 𝛽-decay + Generalized equation:
‘Atoms emit beta particles through a process known as beta decay.
Beta decay occurs when an atom has either too many protons or too
many neutrons in its nucleus.’
It is denoted by symbol 𝛽.
𝐙
𝐀
𝐗 → 𝐙+𝟏
𝐀
𝐘 /𝒁−𝟏
𝑨
𝒀 + 𝐞− /𝐞+
 𝒁
𝑨
𝑿 is the parent nucleus.
 A is the total number of nucleons.
 Z is the total number of protons.
 𝒁+𝟏
𝑨
𝒀 / 𝒁−𝟏
𝑨
𝒀 are the daughter nucleus for –ve beta decay and +ve beta decay
 e-,e+ are the released beta particles for –ve beta decay and +ve beta decay
 Respectively.

Neutrino Hypothesis:
We can calculate the amount of energy whenever a nuclear reaction takes place. We also
calculate the kinetic energy of the emitted particle. Here we theoretical predicted kinetic
energy of the electron. But experimentally the electron has continuous distribution of
kinetic energy.
We perform an experiment in which we have kinetic
energy of the particle but there exist a missing energy
in compare of maximum expected kinetic energy.
It can be seen that there is the violation of law of
conservation of energy(complete energy is not present
there is a missing kinetic energy).
There occur three types of basic violations;(Wolf-Pouli notice in 1931)
1) Law of conservation of energy 2) law of conservation of linear momentum
3) law of spin angular momentum
Expected
K.E.
on
theoretical
base
K.E. of
particl
e
Missin
g
energy

1) Law of conservation of energy- As the total energy is not present there is missing
energy
2) law of conservation of linear momentum- The recalling particle and the emitted
particle (e-) should move in the same direction.
But here 𝟔
𝟏𝟐
𝐂 ← 𝟓
𝟏𝟐
𝐁
3) law of spin angular momentum- here we have 𝐧 → 𝐩 + 𝐞−
} they all are fermions
Which means each have half spin. 𝟏
𝟐
𝟏
𝟐
𝟏
𝟐 but it is not balanced.
E.Fermi in 1934 give a solution that there exist an other particle.
1) It should be neutral (from above equation the charge is balanced).
2) Tiny mass/ small rest mass.
3) Must have half spin so. It should be a fermion.
They gave it the name NEUTRINO(little neutral one).
Neutrino because spin and spin angular momentum are in opposite direction.
Antineutrino because spin and spin angular momentum are in same direction.
𝒆−

Types of beta decay:
Beta-Minus Decay:
 Negative beta decay releases a
negatively charged beta particle called
an electron and an antineutrino.
 𝐙
𝐀
𝐗 → 𝐙+𝟏
𝐀
𝐘 + 𝐞−
+𝝊
 A neutron is transformed to yield a
proton.
 N→ 𝐩 + 𝐞−
+ 𝛖
Beta-Plus Decay:
 Positive beta decay releases a positively
charged beta particle called a positron,
and a neutrino.
 𝐙
𝐀
𝐗 → 𝐙−𝟏
𝐀
𝐘 + 𝐞+
+𝝊
 The proton disintegrates to yield a
neutron.
 P→ 𝐧 + 𝐞+
+ 𝛖

Table:
Symbol Charge Mass
Ionization
energy
Nature of
radiation
Relative
penetrating
power
𝜷 1- 𝟗. 𝟏 × 𝟏𝟎−𝟐𝟖𝒈
intermediat
e
electron 100
Beta decay

Examples:
The 𝛽 − decay of carbon-14 is;
𝟔
𝟏𝟒
𝑪 → 𝟕
𝟏𝟒
𝑵 + −𝟏
𝟎
𝒆−
In this example, a neutron of carbon is
converted into a proton and the emitted beta
particle is an electron.
The β+ decay of carbon-10 is;
𝟓
𝟏𝟎
𝑪 → 𝟔
𝟏𝟎
𝑵 + 𝟏
𝟎
𝒆+
In this example, a proton of carbon is converted
into a neutron and the emitted beta particle is a
positron.

Summary:
Beta decay occurs in two way
positive beta decay and negative
beta decay. The electron or positron
emits plus the energy released in
the form of neutrino or antineutrino.
The atom become stable after the
beta decay process.

𝛾-decay
2. History
3. State alpha decay + Generalized
equation
4. Explanation of alpha decay
5. Diagram + Table +
6. Examples
7. Summary

History:
Paul Villard, a French chemist and physicist, discovered gamma
radiation in 1900, while studying radiation emitted from radium. In 1914,
gamma rays were observed to be reflected from crystal surfaces, proving
that they were electromagnetic radiation.

State 𝛾-decay + Generalized equation:
‘A nucleus changes from a higher energy state to a lower
energy state through the emission of electromagnetic radiation.
Gamma rays cannot deflected by magnetic or electric field.’
It is denoted be symbol 𝛾.
𝐙
𝐀
𝐗∗ → 𝐙
𝐀
𝐗 + 𝟎
𝟎
𝛄
 𝐙
𝐀
𝐗∗
is the exited atom.
 𝐙
𝐀
𝐗 is the relaxed state of initial atom.
 𝟎
𝟎
𝛄 is the released gamma ray photon.

Table:
Symbol Charge Mass
Ionization
energy
Nature of
radiation
Relative
penetrating
power
𝜸 0 0 Very high
High
energy
photons
10,000
Gamma-decay

Explanation of 𝛾–decay:
 Most of the time, gamma decay occurs after the radioactive
nuclei have undergone an alpha or a beta decay.
 The alpha and beta decays leave the daughter nuclei in an
excited state. From the excited state, the daughter nuclei can
get back to the ground state by emitting one or more high
energy gamma rays.
𝟗𝟐
𝟐𝟑𝟖
𝐔 → 𝟗𝟎
𝟐𝟑𝟒
𝐓𝐡∗
+ 𝟐
𝟒
𝐇𝐞
𝟗𝟎
𝟐𝟑𝟒
𝐓𝐡∗
→ 𝟗𝟎
𝟐𝟑𝟒
𝐓𝐡 + 𝟎
𝟎
𝛄
𝟐𝟕
𝟔𝟎
𝑪𝒐 → 𝟐𝟖
𝟔𝟎
𝑵𝒊∗ + 𝒆− + 𝝊
𝟐𝟖
𝟔𝟎
𝑵𝒊∗
→ 𝟐𝟖
𝟔𝟎
𝑵𝒊 + 𝟎
𝟎
𝜸
 The spectra of gamma ray indicates that a nucleus can have
several excited states, when an excited state return to its
normal state gamma rays emitted.
Emission of
𝜸 −after 𝜷-decay
Emission of
𝜸 −after 𝜶-decay

Examples:
The 𝛾-decay of barium-137.
𝟓𝟔
𝟏𝟑𝟕
𝑩𝒂∗ → 𝟓𝟔
𝟏𝟑𝟕
𝐁𝐚 + 𝟎
𝟎
𝛄
In this example the parent atom is
lowered in energy.
The 𝛾 −decay of plutonium-240.
𝟗𝟒
𝟐𝟒𝟎
𝑷𝒖∗ → 𝟗𝟒
𝟐𝟒𝟎
𝐏𝐮 + 𝟎
𝟎
𝛄
In this example the parent atom is
lowered in energy.
*

Summary:
The number of protons (and
neutrons) in the nucleus does not
change in this process, so the
parent and daughter atoms are the
same chemical element.’

Result:
Alpha, beta and gamma decay are
a result of the three fundamental forces
working in the nucleus – the 'strong' force, the
'weak' force and the 'electromagnetic' force.
In all three cases, the emission of radiation
increases the nucleus stability, by adjusting its
proton/neutron ratio.

Thank You 
Hope For The Best

State and explain Alpha , Beta and Gamma decay

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