Chapter 30.2, Problem 25PP

To determine

The mass of tritium after $24.6\text{ years}$ .

Answer to Problem 25PP

  $N(t=24.6\text{ years})=0.25\text{ g}$

Explanation of Solution

Given:

Initial mass, $N_0=1\text{ g}$

Half- life of tritium, $t_{1/2}=12.3\text{ years}$

Formula used:

  $N(t)=N_0{\left(\frac{1}{2}\right)}^n$

Where, $N(t)$ = amount at given time

  $n$ = number of half lives

  $N_0$ = initial amount

Calculation:

The number of half -lives is calculated as,

  $\begin{array}{l}n\times t_{1/2}=24.6\\ n=\frac{24.6}{12.3}\\ n=2\text{ years}\end{array}$

The mass of tritium after $24.6\text{ years}$ is calculated as,

  $\begin{array}{l}N(t)=1{\left(\frac{1}{2}\right)}^2\\ N(t=24.6\text{ years})=1\left(\frac{1}{4}\right)\\ N(t=24.6\text{ years})=0.25\text{ g}\end{array}$

Conclusion:

The mass of tritium after $24.6\text{ years}$ is $0.25\text{ g}$ .