Define half life period of a radioactive sample. Arrive at the relation between half life and decay constnat.

Explanation

It is the time during which half of the atoms of radioactive substance undergo disintegration
Consider the relation, `N=N_(0)e^(-lambda t)…(1)`
Where `N_(0)` = initial number of atoms in a radioactive substance.
N=Number of atoms at given instant t.
`lambda` = Decay constant.
For half life period
`t=T_((1)/(2))` and `N=(N_(0))/(2)`
`(1)implies(N_(0))/(2)=N_(0)e^(-lambda T_((1)/(2)))`
`(N_(0))/(2)=(N_(0))/(e^(lambda T_((1)/(2)))`
`lambda T_((1)/(2))=log_(e)2" "[because e^(x)=yimpliesx=log_(e)(y)]`,
`lambdaT_((1)/(2))=2.303log_(10)(2)`
`lambda T_((1)/(2))=2.303xx0.3010`
`T_((1)/(2))=(0.693)/(lambda)`