Question

The radioisotope, tritium $ (_{1}^{3}H) $ has a half-life of 12.3 yr. If the initial amount of tritium is 32 mg, how many milligrams of it would remain after 49.2 yr?

• A. 4 mg
• B. 8 mg
• C. 1 mg
• D. 2 mg

Answer 1

Answer: (D)

Half-life $ ({{t}_{1/2}})=12.3\,yr. $ Initial amount $ ({{N}_{0}})=32\,mg $ Amount left (N) =? Total time $ (T)=49.2\,yr $ $ \frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}} $ where $ n= $ total number of half-life $ \eta =\frac{\text{Total}\,\text{time}}{\text{Half }-\text{life}} $ So, $ \frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}} $ $ \frac{N}{32}={{\left( \frac{1}{2} \right)}^{4}} $ $ \frac{N}{32}=\frac{1}{16} $ $ N=\frac{32}{16}=2\,mg $ aHalf-life $ ({{t}_{1/2}})=12.3\,yr. $
Initial amount $ ({{N}_{0}})=32\,mg $
Amount left (N) =?
Total time $ (T)=49.2\,yr $
$ \frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}} $
where $ n= $ total number of half-life
$ \eta =\frac{\text{Total}\,\text{time}}{\text{Half }-\text{life}} $
So, $ \frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}} $
$ \frac{N}{32}={{\left( \frac{1}{2} \right)}^{4}} $
$ \frac{N}{32}=\frac{1}{16} $
$ N=\frac{32}{16}=2\,mg $