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. 10
B. 20
C. 5
D. 2.5

Answer

A

Explanation

Activity of radioactive substance, `A=A_(0)e^(-lambdat)`
`rArr" "(A)/(A_(0))=e^(-(0.693)/(T_(1//2)))" "[becauseT_(1//2)=(0.693)/(lambda)]`
`rArr" "(1)/(16)=e^(-(0.693xx40)/(T_(1//2)))rArr(0.693xx40)/(T_(1//2))=ln16`
`rArr" "T_(1//2)=(0.693xx40)/(ln 16)=9.997~~"10 days"`