In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life ?

Options

A. 0.37
B. 0.5
C. 0.55
D. 0.63

Answer

D

Explanation

The number of radioactive nuclei after time t is given by
`(N)/(N_0) = e^(-lamdat)`
In this case t = one meanlife `(tau)`
But `tau = 1/lamda therefore t = 1/lamda`
`therefore N = N_0 e^(-txx1//t) = N_0e^(-1) = (N_0)/(e ) = (N_0)/(2.71)`
`therefore N_0 = 0.37 N_0`
`therefore` No. of radioactive nuclei decaying in time `tau`
`=N_0 - 0.37N_0 = 0.63N_0`
`therefore` percentange of nuclei decaying in time `tau` = 63%