Chapter 30, Problem 30P

To determine

The amount of energy released in electron capture by Beryllium. ${}_4{}^7\text{B}\text{e}+e^{-}\to {}_3{}^7\text{L}\text{i}+\nu$

Answer to Problem 30P

Solution:

The amount of energy released in electron capture by Beryllium is $\text{1}\text{.374 MeV}\text{.}$

Explanation of Solution

Formula used:

Binding energy is $\Delta m{c}^2$.

Solution:

Calculation:

Mass of ${}_4{}^7\text{B}\text{e}$ is $7.016929\text{u}$. Mass of ${}_3{}^7\text{L}\text{i}$ is $7.016003\text{u}$. Mass of electron is $0.0005486\text{u}$. Mass defect is $\Delta m=7.016929\text{u}+0.0005486\text{u}-7.016003\text{u}=\text{0}\text{.0014746}\text{u}$

Energy released is $\text{0}\text{.0014746}\text{u}\times \frac{931.5\text{MeV}}{\text{u}}=1.374\text{MeV}$

Conclusion:

Mass is equivalent to energy. Mass in a decay reaction cannot increase. The change in mass appears as energy.The amount of energy released in electron capture by Beryllium is $\text{1}\text{.374 MeV}\text{.}$