Chapter 30.2, Problem 26PP

To determine

The remaining mass of neptunium on Tuesday of next week.

Answer to Problem 26PP

The remaining mass of neptunium on Tuesday of next week is $0.25\text{ g}$ .

Explanation of Solution

Given:

The mass of neptunium on Monday of current week, $N_0=4\text{ g}$

Half - life, $t_{1/2}=2\text{ days}$

Formula used:

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

Where, $N(t)$ = remaining mass

  $N_0$ = initial mass

  $n$ = number of half lives

Calculation:

The total number of days from current week of Monday to next week of Tuesday is $8$ days.

So, the number of half- lives is,

  $\begin{array}{l}n=\frac{\text{Total days}}{t_{1/2}}\\ n=\frac{8}{2}\\ n=4\end{array}$

The amount of mass remaining on next week of Tuesday is:

  $\begin{array}{l}N(t)=N_0{\left(\frac{1}{2}\right)}^n\\ N(t)=4{\left(\frac{1}{2}\right)}^4\\ N(t)=4\times 0.0625\\ N(t)=0.25\text{ g}\end{array}$

Conclusion:

The amount of remaining of Tuesday is $0.25\text{ g}$ .