Estimate the number of mean lives elapsed, when the number of atoms in a radioactive sample decrease to 5% of the original value.

Explanation

Let the required number of mean lives elapsed be .m., then
`t=m lt tau gt=m/lambda`
N=5% of `N_0=1/20N_0`
But, `N=N_0e^(-lambdat)`
`therefore N_0/20 = N_0 e^(-m)` or , `e^m`=20
or , m=ln 20 = ln 2+ ln 10 = 0.693 + 2.303 `approx` 3
`therefore` At the end of about three average lives, the number of atoms (undecayed) would fall to 5%.