**Balanced Equation**

- In α decay, the nucleon number decreases by 4; proton number decreases by 2.
- In β
^{– }decay, the nucleon number is unchanged, the proton number increases by 1. - In β
^{+}decay, the nucleon number is unchanged; the proton number decreases by 1. - In γ emission, no change in nucleon and proton number.

**Einstein’s Mass-Energy equation**

It links energy and mass. The equation is;

E = mc^{2}

Where c is 3.00 × 10^{8} ms^{-1}

The mass of the system increases when energy is supplied to it and when energy is releases from the system, mass decreases.

ΔE = Δmc^{2}

The mass defect of a nucleus is equal to the difference between total mass of the individual, separate nucleons and the mass of the nucleus.

The loss in mass implies that energy is released.

**Another unit of Mass**

1Atomic mass unit is defined as 1/12 of the mass of neutral atom of carbon-12. i.e. 1u = 1.6605 × 10^{-27}

**Energy released in radioactive decay**

Here, we take the example of decay of nucleus of uranium- 238

^{238}_{92}U———–>^{234}_{90}Th + ^{4}_{2}He

Mass of ^{238}_{92}U nucleus = 3.95283 × 10 ^{-25}

Total mass of ^{234}_{90}Th nucleus and ^{4}_{2}He = 3.95276 × 10^{-25} kg

Change in mass Δm = -7.0 × 10^{-30} kg

Hence energy released in decay:

Energy released 6.3 × 10^{-13} J

**Binding Energy **

It is the minimum energy needed to pull a nucleus apart into its separate nucleons. The greater the value of the binding energy per nucleon, the more tightly bounded the nucleons that make up the nucleus.

**Nuclear fission**

In this case the heavy nucleus splits into two smaller nuclei.

Binding energy of parent nucleus is less than the sum of the two binding energies fragments.

**Nuclear Fusion**

The process by which two very light nuclei join together to for a heavier nucleus. The binding energy of parent nuclei is less than the final binding energy nucleus of the product.

**Decay Constant and Half-Life**

Decay Constant (λ) is the probability that an individual nucleus will decay per unit time interval. Its unit are h^{-1} or s^{-1} or per day or per year.

Radioactive decay follows an exponential decay pattern.

A= ΔN/Δt

The half-life t_{1/2 }of a radioisotope is the mean time taken for the half of the active nuclei in a sample to decay.

In time equal to one half-life, the number of undecayed nuclei is also halved;

N = N_{0 }e^{(-}^{λ}^{t)}

N/N_{0} = e^{(-}^{λ}^{t1/2)} = ½

So, e^{(}^{λ}^{t1/2)} = 2

Or, λ = In 2 ≈ 0.693

Hence, λ = 0.693/t_{1/2}

Therefore, the half-life and decay constant are inversely proportional to each other.