Name: Radioactive Decay
Uploaded: 2019-07-19
Duration: 5 min 38 s
Description: When an atom undergoes radioactive decay, it will emit a particle and some energy. But how is the nucleus affected when radioactive decay takes place? Find o...

Question

What is mean life of a radio active element?

Accepted Answer

Mean life is the average lifetime of all the nuclei of a particular unstable atomic species. This is the sum of the lifetimes of all the individual unstable nuclei in a sample, divided by the total number of unstable nuclei present. It can be written as

$τ = \frac{\int_{0}^{N_{0}} t dN}{N_{0}}$ where $N_{0}$ =initial number of nuclei, $N$ = number of nuclei after the time $t$ .

The other relations are,

$T_{\frac{1}{2}} = \frac{\ln 2}{λ} = \frac{0.693}{λ} = 0.693 τ$ , Where $T_{\frac{1}{2}}$ = radioactive half life, $λ$ = decay constant $τ$ = mean life

The average lifetime is the reciprocal of the decay constant i.e $τ = \frac{1}{λ}$

What is mean life of a radio active element?

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