7/8 of the original mass of a radioactive substance decays in 30 min. What is the half life of the radioactive substance ?

Options

A. 5 min
B. 7.5 min
C. 10 min
D. 15 min

Answer

C

Explanation

`(7)/(8)` of the original mass decays in 30 min.
`therefore` Mass left after 30 min `= (1)/(8)` of the original mass
`therefore" "(N)/(N_(0)) = (1)/(8)`
Using `(N)/(N_(0)) = ((1)/(2))^(n) therefore (1)/(8) = (1)/(2^(3)) = (1)/(2^(n))`
`therefore" "n = 3` = No. of half lives
`therefore` Half life `= ("Total time")/("No. of half lives") = (30)/(3) = 10` min