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 $(t_{1/2})=12.3yr.$ Initial amount $(N_0)=32mg$ Amount left (N) =? Total time $(T)=49.2yr$ $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$ where $n=$ total number of half-life $\eta =\frac{\text{Total}\text{time}}{\text{Half }-\text{life}}$ So, $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$ $\frac{N}{32}={\left(\frac{1}{2}\right)}^4$ $\frac{N}{32}=\frac{1}{16}$ $N=\frac{32}{16}=2mg$ aHalf-life $(t_{1/2})=12.3yr.$
Initial amount $(N_0)=32mg$
Amount left (N) =?
Total time $(T)=49.2yr$
$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$
where $n=$ total number of half-life
$\eta =\frac{\text{Total}\text{time}}{\text{Half }-\text{life}}$
So, $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$
$\frac{N}{32}={\left(\frac{1}{2}\right)}^4$
$\frac{N}{32}=\frac{1}{16}$
$N=\frac{32}{16}=2mg$