Question

The binding energy per nucleon for $C^{12}$ is $7.68\text{MeV}$ and that for $C^{13}$ is $7.5\text{MeV}$. The energy required to remove a neutron from $C^{13}$ is

• A. $5.34\text{MeV}$
• B. $5.5\text{MeV}$
• C. $9.5\text{MeV}$
• D. $9.34\text{MeV}$

Answer 1

The correct option is A $5.34\text{MeV}$

For $C^{13}$:

Binding energy per nucleon $=7.5\text{MeV}$

$\therefore$ Binding energy$=13\times 7.5=97.5\text{MeV}$

For $C^{12}$:

Binding energy per nucleon$=7.68\text{MeV}$

$\therefore$ Binding energy $=12\times 7.68=92.16\text{MeV}$

We have,

${}_6{C}^{13}{\to }_6{C}^{12}{+}_0{n}^1$

Energy required to remove a neutron,

$\Delta E=97.5-92.16=5.34\text{MeV}$

Hence, $\left(A\right)$ is the correct answer.