The activity of a radioactive nucleide `(X^(100))` is 6.023 curie. If its disintegration constant is `3.7xx10^(10) "sec"^(-1)` , the mass of X is

Options

A. `10^(-3)` g
B. `10^(-15)` g
C. `10^(-6)` g
D. `10^(-14)` g

Answer

B

Explanation

`lambdaN_(t)=A`, where `lambda` is disintegration constant
`N_(t)` =amount of X left after time t
A=activity in curie
`[because` 1 curie `=3.7xx10^(10)` distintegration per sec]
`N_(t)=(6.023xx3.7xx10^(10))/(3.7xx10^(4))=6.023 xx 10^(6)`
Now `6.023xx10^(23)` atoms =100g
`6.023xx10^(6)` atoms `=(100xx6.023xx10)/(6.023xx3xx10^(23))`
`=100xx10^(-17)=10^(-15)g`