Calculate the no. of disintegrations which 1 g of radioactive element X-200 undergoes per sec. `t_(1//2)` of X =1000 years.

Options

A. `3.66 xx 10^(10)` dps
B. `6.6 xx 10^(10)` dps
C. `10^(11)` dps
D. `1.0 xx 10^(10)` dps

Answer

B

Explanation

`t_(1//2) = 1000` years
`=1000xx365xx24xx60xx60s`
`=3.15 xx 10^(10)s`
`lambda=(0.693)/(t_(1//2))=(0.693)/(3.15xx10^(10))`
Mass of sample =1 g
No. of atoms in the sample ,
`n=(1xx6.02xx10^(23))/(200)=3.01xx10^(21)`
Rate=`lambda N`
`=(2.2xx10^(-11))xx(3.01xx10^(21))`
`=6.62 xx 10^(10)` dps