Chapter 30, Problem 37P

To determine

(a) To determine:

Decay constant of uranium

Answer to Problem 37P

Solution:

$4.9\times {10}^{-18}{\sec }^{-1}$

Explanation of Solution

Given Info:

Half-life of ${}_{92}{}^{238}U$ is $4.5\times {10}^{9}year$. Decay constant of another nucleus is $3.2\times {10}^{-5}{s}^{-1}$

Formula Used:

$T_{1/2}=\frac{\ln 2}{\lambda }$

Where $T_{1/2}$ is half-life and $\lambda$ is decay constant.

Calculation:

Decay constant and half-life are related according to the given equation

$\begin{array}{l}{T}_{1/2}=\frac{\ln 2}{\lambda }\\ \lambda =\frac{\ln 2}{T_{1/2}}=\frac{\ln 2}{4.5\times {10}^{9}years}\\ =1.5\times {10}^{-10}y{r}^{-1}=4.9\times {10}^{-18}{\sec }^{-1}\end{array}$

To determine

(b) To determine:

Half-life of nucleus

Answer to Problem 37P

Solution:

$2.2\times {10}^{4}s\approx 6hr$

Explanation of Solution

Calculation:

Half-life of the nucleus can be calculated as

$\begin{array}{l}{T}_{1/2}=\frac{\ln 2}{\lambda }\\ =\frac{\ln 2}{3.2\times {10}^{-5}{s}^{-1}}\\ =2.2\times {10}^{4}s\approx 6hr\end{array}$