A radioactive sample of `^(238)U` decay to Pb through a process for which the half is `4.5 xx 10^(9)` year. Find the ratio of number of nuclei of Pb to `^(238)U`after a time of `1.5 xx 10^(9)` year Given `(2)^(1//3)= 1.26`

Options

A. 0.12
B. 0.26
C. 1.2
D. 0.37

Answer

B

Explanation

(b) Here `(N)/(N_0) = ((1)/(2))^n = ((1)/(2))^(1//3)`
where `n` = Number of half lives `= (1)/(3)`
`rArr (N)/(N_0) = (1)/(1.26) rArr (N_U)/(N_(Pb) + N_U) = (1)/(1.26)`
`N_(Pb) = 0.26 N_U rArr (N_(Pb))/(N_U) = 0.26`.