8 grams of a radioactive substance is reduced to 0.5 g after 1 hour . The `t_(1//2)` of the radioactive substance is

Options

A. 15 min
B. 30 min
C. 45 min
D. 10 min

Answer

A

Explanation

`N = N_0 (1/2)^(t//T) = N_0 (1/2)^n`
`therefore 0.5 = 8 (1/2)^n therefore (0.5)/(8) = (1/2)^n`
`1/16 = (1/2)^n therefore (1)/(2^4) = (1)/(2^n)`
`therefore n = 4`
`therefore t/T = 4 therefore 1/T = 4`
`therefore T = 1/4 h ` = 15 min.