Half-life is the time required for the amount of something to fall to half its initial value. The converse of half-life is doubling time. The mathematical representation of Half life is given below.

The formula for half life is,

$$t_{\frac{1}{2}}=\frac{ln2}{\lambda }=\frac{0.693}{\lambda }$$

Where,

is half life
is the disintegration constant

Solved Examples

Question 1: Calculate the half life of a radioactive substance whose disintegration constant is 0.002 years^-1 ?

Solution:

Given quantities are,

= 0.002years^-1

Half life equation is,

=

$\begin{array}{l}\frac{0.693}{\lambda }\end{array}$

=

$\begin{array}{l}\frac{0.693}{0.002}\end{array}$

= 346.5 years