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13.Nuclei
hard
A radioactive sample of $U^{238}$ decay to $Pb$ through a process for which half life is $4.5 × 10^9$ years. The ratio of number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 ×10^9$ years (given $2^{1/3} = 1.26$)
A
$0.12$
B
$0.26$
C
$1.2$
D
$0.37$
(IIT-2004)
Solution
(b) Here $\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n} = {\left( {\frac{1}{2}} \right)^{1/3}}$
where $n =$ Number of half lives $ = \frac{1}{3}$
==> $\frac{N}{{{N_0}}} = \frac{1}{{1.26}}$
==> $\frac{{{N_U}}}{{{N_{Pb}} + {N_U}}} = \frac{1}{{1.26}}$
==> ${N_{Pb}} = 0.26\,{N_U}$
==> $\frac{{{N_{Pb}}}}{{{N_U}}} = 0.26$
Standard 12
Physics
