Chapter 30, Problem 43P

To determine

Number of nuclei remaining in the rock

Answer to Problem 43P

Solution:

$N\text{=8}{\text{.5×10}}^{\text{19}}\text{nuclei}$

Explanation of Solution

Given Info:

The activity of the uranium sample is 420 decays per second.

Formula Used:

Activity can be described as

$A=\lambda N$

$A=\frac{\ln 2}{T_{1/2}}N$

Where N is number of particles at time t, λ is decay constant, A is activity and T_1/2 is half-life.

Calculation:

The number of nuclei from the activity of the sample can be determined as

$\begin{array}{l}A=\lambda N=\frac{\Delta N}{\Delta T}\\ A=\frac{\ln 2}{T_{1/2}}N\\ \lambda N=\frac{\ln 2}{T_{1/2}}N\end{array}$

$\begin{array}{l}N=\frac{T_{1/2}}{\ln 2}\frac{\Delta N}{\Delta T}\\ N\text{=}\frac{\text{4}{\text{.468×10}}^{\text{9}}\text{×3}{\text{.156×10}}^{\text{7}}}{\text{ln2}}\text{×420}\\ N\text{=8}{\text{.5×10}}^{\text{19}}\text{nuclei}\end{array}$