Define half life of a radioactive substance.

Explanation

Half life : Half life of a radioactive substance is defined as the time during which the nuclei of half of the atoms of a radioactive substance will decay.
Let `N_(0)` = Number of atoms in a radioactive sample at time `t=0`
and N = Number of atoms in a radioactive sample at time t
We know `N=N_(0)e^(-lambdat)" ....(i)"`
According to definition of half life of a radioactive substance :
When `t=T_(1//2)" then "N=N_(0)//2`
From eqn. (i)
`(N_(0))/(2)=N_(0)e^(-lambdaT_(1//2))`
`implies e^(+lambdaT_(1//2))=2`
Taking log on both sides
`log_(e)e^(lambdaT_(1//2))=log_(e)2`
`lambdaT_(1//2)log_(e)e=2.303log_(10)2`
`lambdaT_(1//2)(1)=2.303xx0.3010`
`T_(1//2)=(0.693)/(lambda)`
which is the required relation between half life of a radioactive substance and decay constant.