# Chapter 31: Nuclear Physics

Balanced Equation

• In α decay, the nucleon number decreases by 4; proton number decreases by 2.
• In βdecay, 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 = mc2

Where c is 3.00 × 108 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 = Δmc2

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

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

23892U———–>23490Th + 42He

Mass of 23892U nucleus = 3.95283 × 10 -25

Total mass of 23490Th nucleus and 42He = 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 t1/2 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 = N0 e(-λt)

N/N0 = e(-λt1/2) = ½

So, e(λt1/2) = 2

Or, λ = In 2 ≈ 0.693

Hence, λ = 0.693/t1/2

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