Chapter 30, Problem 38P

To determine

Half-life of the radioactive material

Answer to Problem 38P

Solution:

1.2 Hours

Explanation of Solution

Given Info:

Radioactive decay produces 1120 decays per minute initially and 3.6 hours later produces 140 decays per minute.

Formula Used:

The exponential decay law for radioactive decay can be described as

$N=N_0{e}^{-\lambda t}$

Where N₀ is the initial number of particles and N is number of particles at time t, λ is decay constant.

Calculation:

Half-life can be calculated as

$\begin{array}{l}N=N_0{e}^{\frac{\ln 2}{T_{1/2}}}\\ T_{1/2}=-\frac{\ln 2}{\ln \frac{N}{N_0}}t=-\frac{\ln 2}{\ln \frac{140}{1120}}\text{(3}\text{.6}\text{h)}\\ \text{=1}\text{.2}\text{hr}\end{array}$