The weight in grams of 1 curie of radioactive element X-200 having a `t_(1//2)` of 69.3 min is

Options

A. `3.0 xx 10 ^(-8)` g
B. `3.7 xx 10 ^(-8)` g
C. `7.4 xx 10 ^(-8)` g
D. 100 g

Answer

C

Explanation

`lambda=(0.693)/(t_(1//2))=(0.693)/(69.3)=10^(-2)` min
1 curie `=3.7xx10^(10)` dps
`(dN)/(dt)=1 Ci =3.7xx10^(10)` dps
`=3.7xx60xx10^(10)` dpm
`=(dN)/(dt)=lambdaN`
`N=(1)/(lambda)*(dN)/(dt)=10^(2)xx3.7xx60xx10^(10)` atoms
`=(3.7xx60xx10^(12))/(6.02xx10^(23))xx200 g`
`=7.375 xx 10^(-8) g`