Radium has atomic weight 226 and a half-life of 1600 Yr. The number of disintegrations produced per second from one gram are

Options

A. `4.8 xx 10^(10)`
B. `9.2 xx 10^(6)`
C. `3.7xx10^(10)`
D. zero

Answer

C

Explanation

Rate of disintegration `=(-dN)/(dt)=lambdaN`
`lambda=(0.693)/(t_(1//2))=(0.693)/(1600xx3.15xx10^(7))S^(-1)`
`(1 "year" =365xx24xx60xx60=3.15 xx 10^(7) "sec")`
`N=N_(0)` (number of Radium nuclei undergoing disintegration )
`=6.02xx10^(23)xx(1)/(226)`
`(-dN)/(dt)=lambdaN`
`=(0.693xx1xx6.02xx10^(23))/(1600xx3.15xx10^(7)xx226)=3.7xx10^(10)`