Chapter 30.2, Problem 27PP

To determine

The activity on June 1.

Answer to Problem 27PP

The activity on June 1 is $5\times {10}^5\text{ Bq}$ .

Explanation of Solution

Given:

Initial activity, $A_0=2\times {10}^6\text{ Bq}$

Half-life, $t_{1/2}=138\text{ days}$

Formula used:

  $A(t)=A_0{\left(\frac{1}{2}\right)}^n$

Where, $A(t)$ = activity at time $t$

  $A_0$ = initial activity

  $n$ = number of half- lives

Calculation:

The total number of days from 1 September to 1 June of next year is:

  $t=273\text{ days}$

The number of half -live is calculated as,

  $\begin{array}{l}n=\frac{273}{138}\\ n=2\end{array}$

The activity on 1 June is:

  $\begin{array}{l}A(t)=2\times {10}^6{\left(\frac{1}{2}\right)}^2\\ A(t)=5\times {10}^5\text{ Bq}\end{array}$

Conclusion:

The activity on 1 June is $5\times {10}^5\text{ Bq}$ .