The life-life of `Bi^210` is `5` days. What time is taken by `(7//8)^th` part of the sample of decay ?

Options

A. 3.4 days
B. 10 days
C. 15 days
D. 20 days

Answer

C

Explanation

`N= N_(0) ((1)/(2))^(1//T), N= N_(0) - (7N_(0))/(8) = (1)/(8) N_(0)`
`therefore (1)/(8) N_(0)`
`therefore (1)/(8) N_(0)= (N_(0)) ((1)/(2))^((t)/(5))`
`rArr ((1)/(2))^(3) = ((1)/(2))^((t)/(5)) rArr 3 = (t)/(5) rArr t= 15` days