One of the harzards of nuclear explosion is the generation of `""^(90)Sr`and its subsequent incorporation in bones. This nuclide has a half-life of 28.1 years. Suppose one microgram was absorbed by new born child, how much `""^(90)Sr` will remain in his bones after 20 years.

Options

A. `2.4 xx 10^(-7)` g
B. `4.2 xx 10^(-6)` g
C. `6.1 xx 10^(-7)` g
D. `1.6 xx 10^(-7) ` g

Answer

C

Explanation

Given `t_(0.5)` for `""^(90)Sr = 28.1` years, `N_(0) = 10^(-6) gm t = 20` years, N = ?
`lambda = (0.693)/(t_(0.5)) = (0.693)/(28.1) = 2.466 xx 10^(-2)` years Also `t = (2.303)/(lambda) log "" (N_(0))/(N)`
`20 = (2.303)/(2.466 xx 10^(-2)) log ""(10^(-6))/(N) " "N = 6.1 xx 10^(-7)` g