Nuclear Chemistry

Nuclear chemistry is a branch of chemistry that focuses on nuclear reactions, radioactivity, nuclear processes, and nuclear properties. It encompasses the study of radioactive materials and their applications in various fields.

1.0Stability of the Nucleus

While some atomic nuclei are stable, others are not. The stability of an atom has often been described in terms of Coulombic forces—attractive and repulsive forces among charged particles. However, these forces alone can't fully explain nuclear stability due to the presence of similarly charged particles (protons) within the nucleus. As a result, there's no universal rule that can predict whether a particular nucleus will be radioactive or how it may undergo decay.

2.0Mass Defect

The mass defect is defined as the difference between the mass of a nucleus and the total mass of its individual nucleons (protons and neutrons). This discrepancy arises because a portion of the mass is converted into binding energy that holds the nucleus together.

3.0Binding Energy

Binding energy is the total energy released when nucleons (protons and neutrons) combine to form a stable nucleus. It reflects the strength of the forces holding the nucleus together. A higher binding energy indicates a more stable nucleus, while a lower binding energy implies less stability.

The formula for binding energy (B.E.) is:

B.E.=Δm×c²

(when mass is in grams, c in cm/sec)

Where:

• Δm = mass defect
• c = speed of light =2.9979×10¹⁰ cm/sec

Now, calculating step-by-step:

B.E.=1.6605×10⁻²⁴×Δm′×(2.9979×10¹⁰)² erg\

=14.923×10⁻⁴×Δm′ erg

=14.923×10−11×Δm′ Joules(since 107 erg=1 J)

$=\frac{14.923\times 10^{-11}\times \Delta m^{\prime }}{1.602\times 10^{-19}\text{eV}}$

$=14.923\times 10^{-4}\times \Delta m^{\prime }\text{erg}=14.923\times 10^{-11}\times \Delta m^{\prime }\text{J}(\text{as }10^7\text{erg}=1\text{J})$

$=\frac{14.923\times 10^{-11}\times \Delta m^{\prime }}{1.602\times 10^{-19}}\text{eV}$

Now, converting to MeV (1MeV=$10^6$eV)

$=\frac{14.923\times 10^{-11}\times \Delta m^{\prime }}{1.602\times 10^{-19}\times 10^6}\text{MeV}$

$\approx 931.478\times \Delta m^{\prime }\text{MeV}$

Binding Energy Per Nucleon

$\bar{B}=\frac{\text{Total Binding Energy}}{\text{Number of Nucleons}}$

The binding energy per nucleon increases with the atomic number and reaches a maximum value for iron-56 (Fe₂₆⁵⁶​) at 8.78 MeV. Beyond iron, the binding energy per nucleon gradually decreases and becomes nearly constant around 7.6 MeV for heavy elements like lead (Pb₈₂^208​) and heavier nuclei..

4.0Nuclear Forces

Protons and neutrons located in the nucleus are called nucleons. The forces that hold them together are known as nuclear forces.
These are short-range forces that act over very small distances—about 1 fermi.

Nuclear forces are immensely stronger than electrostatic forces.
Protons and neutrons are bonded by the rapid exchange of particles known as mesons.
Mesons can be positively charged (π⁺), negatively charged (π⁻), or neutral (π⁰).

5.0Radioactivity

Certain nuclei emit radiation on their own. Such nuclei are known as radioactive, and this spontaneous emission is termed radioactivity.

Types of Radioactive Radiation:

• Alpha (α) Rays: Positively charged rays that bend toward the negative plate.
• Beta (β) Rays: Negatively charged rays that bend toward the positive plate.
• Gamma (γ) Rays: Neutral rays that pass straight without deflection in electric fields.

Alpha Radiation:
An alpha particle, similar to a helium nucleus, contains two protons and two neutrons.
When an α-particle is emitted, the atomic mass drops by 4 units.

Beta Radiation:
A neutron converts into a proton and emits an electron, or a proton converts into a neutron emitting a positron.
During β-emission, the atom’s mass remains the same, but the atomic number increases by one.

Gamma Radiation:

This involves the emission of energy from the nucleus without any particle being released.
Gamma rays don’t change the atom’s mass or atomic number.

Properties of Alpha, Beta, and Gamma Rays

6.0Radioactive Disintegration

This is the conversion of a radioactive nucleus into another nucleus via emission of α, β, or γ rays.

Modes of Disintegration

• Alpha Decay: Emission of an α-particle reduces atomic number by 2 and mass by 4.
  Number of α-particles emitted =
• Beta Decay: Emission of a β-particle increases atomic number by 1, no change in mass.
  Produces isotopes.
  Number of β-particles emitted =
• Gamma Decay: Emission of γ-rays does not alter atomic or mass numbers.

Rate of Disintegration

It’s the number of radioactive atoms decaying per unit time.

Rate of decay =
Or
N=N₀e^−kt

Where,
N_0​ = initial number of atoms
N = atoms after time t

All radioactive decays follow first-order kinetics. Radioactive elements have infinite lifespan.

Half-Life Period:
Time taken for half of a radioactive sample to disintegrate.

Half-life relation:
T=n×t_1/2

 Where n=log⁡(N₀/N)/log⁡2

N₀​ = original amount
N = remaining amount after time T

Average Life:
(Usually given by t=1/k)

Activity of a Radioactive Substance:
Defined as the number of disintegrations per second.
Higher activity = faster decay.

Activity = kN

Where N is the number of atoms and
N_A​ = Avogadro’s number = 6.022×10²³

7.0Radioactive Disintegration Series

8.0Nuclear Reactions

• Nuclear Fission: A heavy nucleus splits into smaller ones, releasing large energy.
• Nuclear Fusion: Two light nuclei combine to form a heavier one, releasing massive energy.

9.0Applications of Radioactivity

1. Estimating the Age of Objects (Dating Techniques):

• Carbon Dating:
  Used to determine the age of archaeological and biological specimens by measuring the amount of carbon-14 present.
• Uranium Dating:
  Used for estimating the age of rocks and the Earth by analysing the decay of uranium isotopes.

2. Medical Applications:

Therapeutic Use:
Radioactive isotopes are employed in various treatments, including cancer therapy, where radiation is used to target and destroy malignant cells.