Chapter 30, Problem 20P

To determine

Part (a):

The amount of energy required to remove a proton from ${}_7{}^{15}\text{N}$.

Answer to Problem 20P

Solution:

The amount of energy required to remove a proton from ${}_7{}^{15}\text{N}$ is $10.21\text{MeV}$.

Explanation of Solution

Formula used:

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

Calculation:

When ${}_7{}^{15}\text{N}$ loses one proton it becomes ${}_6{}^{14}\text{C}$. When ${}_7{}^{15}\text{N}$ loses one neutron it becomes ${}_7{}^{14}\text{N}$.

Mass of ${}_7{}^{15}\text{N}$ is $15.000109\text{u}$. Mass of ${}_6{}^{14}\text{C}$ is $14.003242\text{u}$. Mass of proton ${}_1{}^1\text{H}$ is $1.007825\text{u}$.

Mass defect is $\Delta \text{m}=14.003242\text{u}+1.007825\text{u}-15.000109\text{u}=\text{0}\text{.010958}\text{u}$.

The amount of energy required to remove a proton from ${}_7{}^{15}\text{N}$ is $\text{0}\text{.010958}\text{u}\times \frac{931.5\text{MeV}}{\text{u}}=10.21\text{MeV}$

To determine

Part (b):

The amount of energy required to remove (b)a neutron from ${}_7{}^{15}\text{N}$.

Answer to Problem 20P

Solution:

The amount of energy required to remove a neutron from ${}_7{}^{15}\text{N}$ is $10.83\text{MeV}$.

Explanation of Solution

Formula used:

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

Calculation:

When ${}_7{}^{15}\text{N}$ loses one proton it becomes ${}_6{}^{14}\text{C}$. When ${}_7{}^{15}\text{N}$ loses one neutron it becomes ${}_7{}^{14}\text{N}$.

Mass of ${}_7{}^{14}\text{N}$ is $14.003074\text{u}$. Mass of neutron ${}_0{}^1\text{n}$ is $1.008665\text{u}$. Mass defect is $\Delta \text{m}=14.003074\text{u}+1.008665\text{u}-15.000109\text{u}=\text{0}\text{.01163}\text{u}$.

The amount of energy required to remove a neutron from ${}_7{}^{15}\text{N}$ is $\text{0}\text{.01163}\text{u}\times \frac{931.5\text{MeV}}{\text{u}}=10.83\text{MeV}$

Protons attract each other via the strong nuclear force at the same time they repel each other

via the electric force. Neutrons, because they are electrically neutral, only attract other neutrons or protons via the strong nuclear force. Hence, the difference in nucleon separation energy.