A nucleus of `Ux_1` has a half life of 24.1 days. How long a sample of `Ux_1` will take to change to 90% of `Ux_1`.

Options

A. 80 days
B. 40 days
C. 20 days
D. 10 days

Answer

A

Explanation

Here, `lambda=0.693/(T_(1//2)) =0.693/24.1=0.02876 "day"^(-1)`
`N=N_0-90%` of `N_0 = N_0/10`
As N=`N_0e^(-lambdat)`
`therefore N_0/10=N_0e^(-lambdat)` or `1/10 = e^(-lambdat)` or `10=e^(lambdat)`
or `log_e10= lambdat`
`therefore t=1/lambda_"log"_e 10=(2.303 log 10)/0.02870 = (2.303xx1)/0.02876 `= 80 days