Radioactive Decay Law: Overview, Questions, Preparation

Radioactive Decay can be defined as the process by which an unstable atom loses its energy by the emission of radiations. It was discovered by Henry Becquerel in 1896. The particles of atoms cannot be combined due to the lost energy of an unstable nucleus. The decay in the isotopes is constant because of the emissions of radiations.

Three types of Radioactive Decay are as follows:

1. Alpha radioactive decay
2. Beta radioactive decay
3. Gamma radioactive decay

It shows the relationship between the number of nuclei and the radioactive decays per unit of the radioactive compounds. Let us quantify the rate of decay by using proportionality.

Let us say that the N is the number of nuclei,

Then ΔN would be the number of radioactive decay for the time Δt

ΔN Δt ∝ N or

ΔN Δt = λN,

Here, λ is the constant of proportionality.

And ΔN is the reduction or the change in the total number of nuclei.

As per convention, it is negative,

∂N ∂t = −λN

It can be written as:

∂N N = − λ∂t

After integrating both sides, we will get:

∫NN0 ∂NN = −λ ∫ tt0 ∂t InN – In N0 = −λ (t – t0)

Here, N0 is the original number of nuclei.

T0, i.e., t = 0

After applying this in the equation, we will get:

In NN0 = − λt

It will give us,

Nt = N0 e – λt

This is exponential decay.

Let us now calculate the rate using the above equation.

It will be,

R = − ∂N ∂t

After substituting it with Nt, we will get:

Nt = N0 e – λt

The differentiation result will be,

R = − ∂N ∂t = λN e – λt0 R = Re – λt0 R0

Here, the rate of decay at the time is, 0

Let us now substitute it in the original equation, and we will get

ΔN Δt = λN

Which is, R = λN

Example 1) Write the equation of radioactive decay.

Answer – The equation of radioactive decay is N = N0 e−λ t N = N0 e − λ t

Question 2) Write the formula of Alpha radioactive decay.

Answer – The formula of Alpha radioactive decay is written as:

                     E = (mi – mf – mp) c2

Here, mi is the initial mass of the nucleus,

The mass of the nucleus after emission of the particles is denoted as mf

And the mass of the emission of the particles is written as mp.

Question 3) Write the meaning of alpha decay.

Answer – Alpha decay is the process when alpha particles emit the nucleus of the alpha itself.

Q: What are the three types of radioactive decay?

Q: What is the unit of radioactive decay?

Q: What is the gray unit of radiation?

Q: Which type of radioactive decay is the most harmful radiation?

Q: What do you mean by Beta radioactive decay?