Question

A sample of radioactive substance has $ 8\times {{10}^{8}} $ nuclei. Its half life is 20 minutes. The number of nuclei that will decay in one hour is

• A. $ 2\times {{10}^{8}} $
• B. $ 4\times {{10}^{8}} $
• C. $ 1\times {{10}^{8}} $
• D. $ 7\times {{10}^{8}} $

Answer 1

Answer: (D)

: For radioactive decay, $ \frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/T}} $ where $ T= $ half life $ N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{t/T}}=(8\times {{10}^{8}})\times {{\left( \frac{1}{2} \right)}^{60/20}}=\frac{8\times {{10}^{8}}\times 1}{8} $ $ =1\times {{10}^{8}}nuclei $ . $ \therefore $ Number of nuclei left undecayed $ =1\times {{10}^{8}} $ $ \therefore $ Number of nuclei that have decayed $ =(8-1)\times {{10}^{8}}=7\times {{10}^{8}} $ .