Consider an initially pure `M gm` sample of `X`, an isotope that has a half-life of `T` hour, what is its initial decay rate (`N_A` = Avogadro No, atomic weight of `X` is `A`)

Options

A. `(M N_(A))/(T)`
B. `(0.693M N_(A))/(T)`
C. `(0.693 M N_(A))/(A T)`
D. `(2.303 M N_(A))/(A T)`

Answer

C

Explanation

`N= N_(0) e^(-lamda t)`
`rArr |(dN)/(dt)|= N_(0) lamda e^(- lamda t)`
at t= 0, `(dN)/(dt)= N_(0) lamda`
`N_(0)= ("Mass of the sample")/("Mass of a single atom") = (M)/(A//N_(A)) = (MN_(A))/(A)`
`therefore |(dN)/(dt)|_(t= 0) = (M N_(A) lamda)/(A)= (0.693M N_(A))/(A T)`