Half-time means the time required for the quantity of a substance to reduce to its half of initial value.

It is used for checking the rate of fall in the value of substances. It is generally helpful in nuclear physics where it describes the rate of radioactive decaying of an atom. The half life formula is derived by dividing 0.693 by lambda (λ) which is a constant. Here, is the disintegration constant i.e., the decay constant. So, the half life formula is given by:

t1/2 = 0.693/, here t1/2= half-life and λ= constant

Suppose N is the number of radioactive atoms at time t. Let dN be the quantity by which the atoms reduce in time dt. So, the rate of change is dN/dt = – λN

On integration, we get N= N0 e-t where N0= size of population initially of radioactive atoms when t=0.

This relationship between half-life, the time period, t1/2, and the decay constant λ is given by t1/2 =0.693/

**Solved Examples**

Q1. The decay constant of a substance is 0.64 s-1. Find the half-life of the substance.

Ans. The half-life formula can be used to find the half-life of the given substance

t1/2 =0.693/

= 0.693/ 0.64

=1.0828.

Hence, half-life of the substance is 1.08 seconds.

Q2. Find the decay constant of a radioactive substance having a half-life of 0.02 seconds.

Ans. t1/2= 0.02 [given]

0.02=0.693/

λ=0.693/0.02

λ=34.65

Therefore, the value of decay constant=34.65 s-1