The mass of 1 curie of U-234 `(t_(1//2)=2*35 xx 10^(5) "years")` is

Options

A. `1*548 xx 10^(3)` g
B. `15*48 g`
C. `1*548 xx 10^(-3)` g
D. `1*548 xx 10^(2)` g

Answer

D

Explanation

`t_(1//2) =2.35 xx10^(5)` years
`=2.35 xx 365xx24xx60xx60xx10^(5)s`
`=7.41xx10^(12) s`
`lambda=(0.693)/(t_(1//2))=(0.693)/(7.41 xx 10^(12))=9.3xx 10^(-14)s^(-1)`
Rate = 1 Ci=`3.7 xx 10^(10) dps`
Let mass of `U_(234)=m g`
No. of atoms in mg of U-234,
`N=(mxx6.02xx10^(23))/(234)=mxx2.57xx10^(21)`
Rate `=lambdaN`
`3.7xx10^(10)=9.3xx10^(-14)xxmxx2.57xx10^(21)`
`m=(3.7xx10^(23))/(9.3xx10^(-14)xx2.57xx10^(21))`
`=1.548 xx 10^(2) g`