A radioactive substance decays to `((1)/(16))^(th)` of its initial activity in 40 days. The half-life of the radioacctive substance expressed in days is

Options

A. 2.5
B. 5
C. 10
D. 20

Answer

C

Explanation

It decays to `1/16` th of initial substances in 40 days.
`A=1/16 A_(0)`
`A/A_(0) =(1/2)^(n)`
Now compare `A/A_(0) =(1/2)^(n) =1/16`
Number of half-life involved in this process.
`nT_(1//2)=t`
`4T_(1//2)=40 rArr T_(1//2)=10` days