Question

$ {{C}^{14}} $ has half-life $ 5700\, year $ . At the end of $ 11400\, years $ , the actual amount left is:

• A. 0.5 of original amount
• B. 0.25 of original amount
• C. 0.125 of original amount
• D. 0.0625 of original amount
• E. 0.03125 of original amount

Answer 1

Answer: (B)

From Rutherford law
$ N = N_0 \big(\frac{1}{2}\big)^n $
where n is number of half-lives
$ n = \frac{11400}{5700} = 2 $
$ \therefore \frac{N}{N_0} = \big(\frac{1}{2}\big)^2 $
$ \Rightarrow \frac{N}{N_0} = \frac{1}{4} = 0.25 $
$ \Rightarrow N = 0.25 N_0 $
$ N = 0.25 $ of original amount.