The half-life of a radioactive element which has only `(1)/(32)` of its original mass left after a lapse of `60` days is

Options

A. 12 days
B. 32 days
C. 60 days
D. 64 days

Answer

A

Explanation

We know, after n half -life, undecayed nuclei left are,
`N=N_(0)((1)/(2))^(n),t=nt_(1//2)`
We have, `(N_(0))/(32)=N_(0)((1)/(2))^(60//T)implies5=(60)/(T)`
`implies` Half- life of a radioactive element, T=120 days