A radioactive sample of $U^{238}$ decays to $Pb$ through a process for which half life is $4.5 imes 10^{9}years$. The ratio of number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 imes 10^{9}years$ (given $2^{1/3} = 1.26$)

Question

A radioactive sample of $U^{238}$ decays to $Pb$ through a process for which half life is $4.5 	imes 10^{9}years$. The ratio of number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 	imes 10^{9}years$ (given $2^{1/3} = 1.26$)

Dr. Abubacker · Accepted Answer

(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 $= \frac{1}{3}$
$\Rightarrow \frac{N}{N_{0}} = \frac{1}{1.26} \Rightarrow \frac{N_{U}}{N_{Pb} + N_{U}} = \frac{1}{1.26}$
$\Rightarrow N_{Pb} = 0.26\ N_{U} \Rightarrow \frac{N_{Pb}}{N_{U}} = 0.26$

Q. A radioactive sample of $U^{238}$ decays to $Pb$ through a process for which half life is $4.5 \times 10^{9}years$. The ratio of number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 \times 10^{9}years$ (given $2^{1/3} = 1.26$)

Explanation

Reviewed by Dr. Abubacker

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