Define the term half-life period and decay constant of a radioactive substance. Write their `S.I` units. Establish the relationship between the two.

Explanation

(i) Half-life period: It is the time during with which half the total number of atoms in radioactive elements `(N_(0))` disintergrates. It is denoted by `t_(1//2)`.
(ii) Decay constant: It is the reciprocal of the time interval in which the number of active nuclei in a radioactive sample reduces to `1//e` times of its initial nuclei. Its `SI` unit is `S^(-1)`.
(iii) Relation: Since `N_(t)=N_(0)e^(-lambdat)`
`:. log_(e )N_(t)=log_(e )N_(0)+log_(e )`
`log_(e )N_(t)-log_(e )N_(0)-lambdatlog e`
`lambdat=log_(e )N_(0)-log_(e )N_(t)" " [ :. log e=1]`
`lambdat="log"_(e ) (N_(0))/(N_(t))`
`lambdat=2.303 log.(N_(0))/(N_(t )) :. t=(2.303)/(lambda)log. (N_(0))/(N_(t ))`
For half-life period, `N_(t)=(N_(0))/(2)` and `t=t_(1//2)`
`:. t_(1//2)=(2.303)/(lambda)log.(N_(0))/(N_(0)//2)=(2.303)/(lambda)log2`
`t_(1//2)=(2.30xx0.3010)/(lambda) :. t_(1//2)=(0.6931)/(lambda)`