Question

$U^{238}$ decays to $T{h}^{234}$ with half life 5 x 10${}^9$ yr .The resulting nucleus is in excited state and hence further emits $\gamma$- rays to come to the ground state. It emits 20$\gamma$ - rays per second. The time after which the emission rate will drop to 5$\gamma$ - rays per second is

• A. $1.25\times {10}^9$ yr
• B. ${10}^{10}$ yr
• C. ${10}^{-8}$ yr
• D. $1.25\times {10}^{-9}$ sec

Answer 1

Answer: (B)

${10}^{10}$ yr

Rate of emission of $\gamma$ rays initial $=20\gamma \frac{rays}{sec}$

Rate of emission of $\gamma$ rays to be known $=5\gamma \frac{rays}{sec}$

Fraction of U-238 left $=\frac{1}{4}$ as the radiation is also $\frac{1}{4}$ left which is directly proportional to amount of U-238 left.

Half lives needed $=(\frac{1}{2}{)}^x=\frac{1}{4}\Rightarrow x=2$
The radiation will drop to $5\gamma$ $\frac{rad}{sec}$ after 2 half-lives i.e., $5\times {10}^9\times 2$ years $={10}^{10}$ years.