Chapter 14, Problem 10MPS

To determine

To Find: Thetime taken by the 50 gram of sample to decay to 5 grams.

Answer to Problem 10MPS

The time taken for the decay is $2.21\text{hr}$ .

Explanation of Solution

Given:

The half-life of carbon eleven is 20 minutes.

Calculation:

Consider the half-life of carbon is.

  $\begin{array}{c}{t}_{\frac{1}{2}}=20\text{min}\\ =\frac{1}{3}\text{hr}\end{array}$

As the radioactive reaction is fast decay then,

  $\begin{array}{c}k=\frac{\ln 2}{\frac{2}{3}}\\ =1.039{\text{h}}^{-1}\end{array}$

The formula to determine the time taken by the decay is,

  $\begin{array}{c}t=\frac{1}{k}\ln \frac{50}{5}\\ =\frac{1}{1.039}\ln \left(\frac{50}{5}\right)\\ =2.21\text{hr}\end{array}$

Thus, the time taken for the decay is $2.21\text{hr}$ .