Starting with a sample of pure `.^66 Cu, 7//8` of it decays into `Zn` in `15 min`. The corresponding half-life is.

Options

A. 10 min
B. 5 min
C. 14 min
D. `7(1)/(2)` min

Answer

D

Explanation

`(N/N_0) = (1/2)^(t//T)`
`because (7N)/(8)` have decayed in 15 min.
`therefore` the matter that is left is `(N_0)/(8) " or " (N)/(N_0) = 1/8`
`therefore 1/8 = (1/2)^3 = (1/2)^(15//T)`
`therefore (15)/(T) = 3 therefore T = 5 ` min.