Question

The half life of \(\mathrm{C}^{14}\) is 5760 years. For a \(200 \mathrm{mg}\) sample of \(\mathrm{C}^{14}\), the time taken to change to \(25 \mathrm{mg}\) is
(A) 11520 years
(B) 23040 years
(C) 5760 years
(D) 17280 years

Answer 1

Ans: (D)
 \(:\left(\frac{M}{M_{0}}\right)=\left(\frac{1}{2}\right)^{n} \Rightarrow\left(\frac{25}{200}\right)=\left(\frac{1}{2}\right)^{n} \Rightarrow\left(\frac{1}{2}\right)^{3}=\left(\frac{1}{2}\right)^{n} \Rightarrow n=3\)
\(\therefore\) Time taken \(=3 \times 5760\) years \(=17280\) years

Answer 2

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Answer 3

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