Question

how is the mean life of a radioactive sample related to its half life?

Answer 1

Dear Student,

To get relation between Mean life and Half life for a radioactive sample

Consider -

$\mathit{H}\mathit{a}\mathit{l}\mathit{f}\mathbf{}\mathit{l}\mathit{i}\mathit{f}\mathit{e}\mathbf{}\mathbf{=}\frac{\mathbf{l}\mathbf{n}\mathbf{2}}{\mathbf{\lambda }}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathbf{}\mathit{M}\mathit{e}\mathit{a}\mathit{n}\mathbf{}\mathit{l}\mathit{i}\mathit{f}\mathit{e}\mathbf{}\mathbf{=}\frac{\mathbf{1}}{\mathbf{\lambda }}$

Here λ is decay constant. Hence,

$\mathit{H}\mathit{a}\mathit{l}\mathit{f}\mathbf{}\mathit{l}\mathit{i}\mathit{f}\mathit{e}\mathbf{}\mathbf{=}\mathbf{ln}\mathbf{}\mathbf{2}\mathbf{(}\mathit{M}\mathit{e}\mathit{a}\mathit{n}\mathbf{}\mathit{l}\mathit{i}\mathit{f}\mathit{e}\mathbf{)}\mathbf{}\mathbf{}\mathbf{}\mathbf{\Rightarrow }\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{H}\mathit{a}\mathit{l}\mathit{f}\mathbf{}\mathit{l}\mathit{i}\mathit{f}\mathit{e}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{6931}\mathbf{}\mathbf{(}\mathit{M}\mathit{e}\mathit{a}\mathit{n}\mathbf{}\mathit{l}\mathit{i}\mathit{f}\mathit{e}\mathbf{)}$

Regards.