U r a n i u m - 238 decays to T h o r i u m - 234 with half-life 5 × 10 9 y r . The resulting nucleus is in the excited state and hence further emits γ -rays to come to the ground state. It emits 20 γ -rays per second. The emission rate will drop to 5 γ -rays per second in

Question

U r a n i u m - 238 decays to T h o r i u m - 234 with half-life 5 × 10 9 y r . The resulting nucleus is in the excited state and hence further emits γ -rays to come to the ground state. It emits 20 γ -rays per second. The emission rate will drop to 5 γ -rays per second in, 1.25 × 10 9 y r, 10 10 y r, 10 - 8 y r, 1.25 × 10 - 9 s

MARKS App · Accepted Answer

Number of emitted γ -rays per second is proportional to no of uranium particles left undecayed fraction of particles undecayed, N N 0 = ( 1 2 ) n Where n is the number of half-lives ⇒ 5 20 = ( 1 2 ) n n = 2 Total time = 2 × 5 × 10 9 years = 10 10 yr

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