(a) The number of nuclei of a given radioactive nucleus, at times `t=0 and t=T`, are `N_0 and (N_(0)//n)` respectively. Obtain an expression for the half life `(T_(1//2))` of this nucleus in terms of n and T.
(b) Identify the nature of the 'radioactive radiations', emitted in each step of the 'decay chain' given below:
`""_(Z)^(A) X to ""_(Z-2)^(A-4) Y to ""_(Z-2)^(A-4) Yto""_(Z-1)^(A-4)W`

Explanation

(a) According to the ( exponential) law of radioactive decay
`N=N_(0)e^(-lambda t)`
Given, `N=N_(0) //n and t=T`
`therefore ((N_0)/(n)) = N_(0) e^(- lambda t)`
or `n=e^(lambda t)`
`therefore lambda = (1 n (n))/( T)`
`therefore` Half life `T_(1//2) (0.693)/( lambda) = (0.693 T)/( 1 n (n))`
(b) (i) `alpha`-rays
(ii) `gamma`-rays
(iii) `beta`- rays.