# Half Life Formula

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

#### Practise This Question

One 10 V, 60 W bulb is to be connected to 100 V line. The required induction coil has self inductance of value (f = 50 Hz)