Chapter SH, Problem 17.10APP

To determine

To calculate:The number of times the half-life of fermium- $255$ is longer than the half-life of hassium- $261$ .

Answer to Problem 17.10APP

The half-life of fermium- $255$ is $7780$ times longer than the half-life of hassium- $261$ .

Explanation of Solution

Given data:

Half-life of hassium- $261$ $=9.3\text{ s}$

Half-life of fermium- $255$ $=20.1\text{ h}$

Calculation:

As per the problem,

Half-life of hassium- $261$ $=9.3\text{ s}$

Half-life of fermium- $255$ $=20.1\text{ h}$

Convert half-life of fermium into seconds using conversion ratio $\frac{3600\text{ s}}{1\text{ h}}=1$

So, Half-life of fermium- $255$ $=20.1\text{ h}\times \frac{3600\text{ s}}{1\text{ h}}=72360\text{ s}$

To find number of times ( n ) half-life of fermium- $255$ is longer than the half-life of hassium- $261$ , divide half-life of fermium by half-life of hassium.

  $n=\frac{72360\text{ s}}{9.3\text{ s}}\approx 7780$

Conclusion:

The half-life of fermium- $255$ is $7780$ times longer than the half-life of hassium- $261$ .