The wt. in g of 1 curie of a radioactive element `""^(200)X` having `t_(1//2)` of 69.3 min is

Options

A. `3.7xx10^(-8)` g
B. 200 g
C. `7.4 xx 10^(-8) g`
D. `3.0 xx 10^(-8) g`

Answer

C

Explanation

`t_(1//2)=69.3 "min"=69.3 xx 60 s = 4158 s`
`lambda=(0.693)/(t_(1//2))=(0.639)/(4158)s^(-1)`
`=1.67 xx 10^(-4) s^(-1)`
Rate =1 Ci=3.7`xx10^(10)` dps
Let mass of radioactive sample = m g
`therefore` No. of atoms in the sample ,
`N=(mxx6.02xx10^(23))/(200)`
`=3.01 m xx 10^(21)`
Rate `=lambda N`
`3.7 xx 10^(10)=(1.67xx10^(-4))xx(3.01 mxx10^(21))`
`m=(3.7xx10^(10))/((1.67xx10^(-4))(3.01xx10^(21)))`
`=7.36xx10^(-8) underline(~)7.4 xx 10^(-8) g`