Question

In one mean lifetime of a radioactive element the fraction of the nuclei that has disintegrated is ______. [e is the base of natural logarithm]

Options

• `1/e`

• `1-1/e`

• e

• e - 1

Answer 1

In one mean lifetime of a radioactive element the fraction of the nuclei that has disintegrated is `bbunderline(1-1/e)`. [e is the base of natural logarithm]

Explanation:

Mean lifetime, `t = 1/lambda`

`(N_0-N_t)/N_0 =(N_0-N_0e^(-lambdat))/N_0=(N_0(1-e^(-lambdat)))/N_0`

`=1-e^(-lambdat)=1-e^(-lambdaxx1/lambda)`

`=1-e^-1 = 1-1/e`