The half life of `._92^238U` undergoing `alpha`-decay is `4.5xx10^9` years. The activity of 1 g sample of `._92^238U` is

Options

A. `1.23xx10^4` Bq
B. `1.23xx10^5` Bq
C. `1.23xx10^3` Bq
D. `1.23xx10^6` Bq

Answer

A

Explanation

`T_(1//2)=4.5xx10^9` years
`=4.5xx10^9xx3.16xx10^7=1.42xx10^17` s
One kmol of any isotope contains Avogadro's number of atoms, so 1 g of `._92^238U` contains
`=1/(238xx10^(-3))"kmol"xx6.025xx10^26` atoms per kmol
`=25.3xx10^20` atoms
Activity, R=`lambdaN`
`=0.693/T_(1//2) N =(0.693xx25.3xx10^20)/(1.42xx10^17)s^(-1)`
`=1.23xx10^(4) s^(-1) =1.23xx10^4` Bq