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,

$t_{\frac{1}{2}}$ is half life

$\lambda$ 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,

$\lambda$ = 0.002years^{-1}

Half life equation is,

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

$t_{\frac{1}{2}}$ = $\frac{0.693}{0.002}$

= 346.5 years