Nuclear Chemistry Question 8

Question: A radioactive element with half-life 6.5 hrs has $ 48\times 10^{19} $ atoms. Number of atoms left after 26 hrs

[BHU 2003]

Options:

A) $ 24\times 10^{19} $

B) $ 12\times 10^{19} $

C) $ 3\times 10^{19} $

D) $ 6\times 10^{19} $

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Answer:

Correct Answer: C

Solution:

$ N _{t}=N _{o}{{( \frac{1}{2} )}^{n}} $

$ =48\times 10^{19}{{( \frac{1}{2} )}^{26/6.5}} $

$ =48\times 10^{19}{{( \frac{1}{2} )}^{4}}=3\times 10^{19} $ .