Chapter SH, Problem 16.9APP

To determine

To calculate: Half-life of cobalt-62.

Answer to Problem 16.9APP

Half-life of cobalt-62 is 1.5 minutes.

Explanation of Solution

Given:

Mass of sample = $1.00\text{ g}$

Mass of cobalt-62 remaining after 3 minutes = $\text{0}\text{.25 g}$

Formula used:

The time in which the isotope becomes half of its original amount is called its half-life.

Calculation:

Half of $1.00\text{ g}$ = $\frac{\text{1}\text{.00 g}}{2}=0.50\text{ g}$ .

Therefore, the time in which $0.50\text{ g}$ of cobalt-62 is left is called its half-life.

  $\text{0}\text{.25 g}$ of cobalt-62 is left in 3 minutes

  $1.00\text{ g}$ of cobalt-62 is left in $3\times 0.25=0.75\text{ minutes}$

  $0.50\text{ g}$ of cobalt-62 is left in $\frac{0.75\text{ minutes}}{0.50}=1.5\text{ minutes}$

Conclusion:

Half-life of cobalt-62 is 1.5 minutes.