Chapter 30, Problem 18P

To determine

Part (a):

The total binding energy and binding energy per nucleon of ${}_3{}^7\text{L}\text{i}$

Answer to Problem 18P

Solution:

Total Binding energy of ${}_3{}^7\text{L}\text{i}$ is $12.42\text{MeV}$. Binding energy per nucleon is $1.774\text{MeV}$.

Explanation of Solution

Formula used:

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

Calculation:

Mass of ${}_3{}^7\text{L}\text{i}$ is $7.016003\text{u}$. Mass of neutron ${}_0{}^1\text{n}$ is $1.008665\text{u}$. Mass of proton ${}_1{}^1\text{H}$ is $1.007825\text{u}$

Mass defect is $\Delta \text{m}=4\left(1.008665\text{u}\right)+3\left(1.007825\text{u}\right)-7.016003\text{u}=\text{0}\text{.042132}\text{u}$.

Total Binding energy $\text{0}\text{.013333}\text{u}\times \frac{931.5\text{MeV}}{\text{u}}=12.42\text{MeV}$.

Binding energy per nucleon is $\frac{12.42\text{MeV}}{7}=1.774\text{MeV}$

To determine

Part (b):

The total binding energy and binding energy per nucleon of ${}_{78}{}^{195}\text{P}\text{t}$.

Answer to Problem 18P

Solution:

Total Binding energy of ${}_{78}{}^{195}\text{P}\text{t}$ is $1,545.7\text{MeV}$. Binding energy per nucleon is $7.93\text{MeV}$.

Explanation of Solution

Formula used:

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

First find the total mass of the constituents of the atom.

Calculation:

Mass of ${}_{78}{}^{195}\text{P}\text{t}$ is $194.964792\text{u}$. Mass of neutron ${}_0{}^1\text{n}$ is $1.008665\text{u}$. Mass of proton ${}_1{}^1\text{H}$ is $1.007825\text{u}$. Mass defect is $\Delta \text{m}=\left(195-78\right)\left(1.008665\text{u}\right)+78\left(1.007825\text{u}\right)-194.964792\text{u}=\text{1}\text{.659363}\text{u}$.

Total Binding energy $\text{1}\text{.659363}\text{u}\times \frac{931.5\text{MeV}}{\text{u}}=1545.7\text{MeV}$.

Binding energy per nucleon is $\frac{1545.7\text{MeV}}{195}=7.93\text{MeV}$