Question

The atomic ratio between the uranium isotopes ${}^{238}U$ and ${}^{234}U$ in a mineral sample is found to be $1.8\times 10^{4}$ . The half life of ${}^{234}U$ is $T _{\frac{1}{2}}(234)=2.5 \times 10^{5}$ years. The half-life of ${ }^{238} U$ is-

• A. $4.5\times 10^{9}$ years
• B. $5.4\times 10^{9}$ years
• C. $4.5$ years
• D. $5.4 \, $ years

Answer 1

Answer: (A)

In radioactive equilibrium
$\lambda _{1}N_{1}=\lambda _{2}N_{2}$
$\frac{N_{1}}{T_{1}}=\frac{N_{2}}{T_{2}} \, $
$T_{2}=\frac{N_{2}}{N_{1}}\times T_{1} \, $
$T_{2}=1.8\times 10^{4}\times 2.5\times 10^{5}$
$T_{2}=4.5\times 10^{9} $ years