`50%` of the amount of a radioactive substance decomposes in `5` years. The time required for the decomposition of `99.9%` of the substance will be

Options

A. `10` years
B. between `10` and `50` years
C. less than `10` years
D. between `49` and `50` years

Answer

D

Explanation

Here, hlaf life, `t_(1//2) = 5` years
Decomposed amount `= 99.9%`
Let the original amount, No `= 100`
Left a amount after time `t, = 100 - 99.9 = 0.1`
`N = 0.1`
`because kt = 2.303 "log"(N_(0))/(N)`
or, `(0.693)/(t_(1//2)) xx t = 2.303 "log"(100)/(0.1)`
or, `(0.693 xx t)/(5) = 2.303 log 10^(3)`
or, `t = (2.303 xx 3 xx 5)/(0.693) = 49.85` years