The half life of radioactive radon is 3.8 days. The time at the end of which `(1//20)^(th)` of the radon sample will remain undecayed (Given `log_10`e=0.4343 ) is

Options

A. `3.8` days
B. `1.65` day
C. `33` day
D. `76` day

Answer

B

Explanation

`M = M_(0)e^(-lambdat) rArr (M_(0))/(20) = M_(0)e^(-lambdat) rArr ln (1/20) = -lambdat`
`rArr ((ln(20))/(ln2)) T_(1//2) = t rArr ((ln(2) + ln(10))/(ln2))T_(1//2) = t`
`rArr t = 16.42` days