A radioactive substance decays to `((1)/(16))^(m)` 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^(-lamdat)`
`implies(A)/(A_(0))=e^(-lamdat)=e^(-(0.693)/(T_(1)//2)t)" "[becauseT_(1//2)=(0.693)/(lamda)]`
`implies(1)/(16)=e^((0.693xx40)/(T_(1)//2))`
`implies(0.693xx40)/(T_(1)//2)=ln16`
`impliesT_(1//2)=(0.693xx40)/(ln16)`
`=9.997~~10` days.