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. `(MN_A)/(T)`
B. `(0.693 MN_A)/(T)`
C. `(0.693 MN_A)/(AT)`
D. `(2.303 MN_A)/(AT)`

Answer

C

Explanation

( c) `N = N_0 e^(-lamda t) rArr |(dN)/(dt)| = N_0 lamdae^(-lamdat)`
Initially at `t = 0,|(dN)/(dt)|_(t = 0) = N_0 lamda`
where `N_0` = Initial number of undecayed atoms
`= ("Mass of the sample")/("Mass of single atom of" X) = (M)/(A//N_A) = (MN_A)/(A)`
`:. |(dN)/(dt)|_(t=0) = (MN_A lamda)/(A) = (0.693 MN_A)/(AT)`.