Question

The binding energy per nucleon for ${\text{C}}^{12}$ is $7.68\text{MeV}$ and that for ${\text{C}}^{13}$ is $7.47\text{MeV}$. The energy required to remove a neutron from ${\text{C}}^{13}$ is

• A. $4.95\text{MeV}$
• B. $2.75\text{MeV}$
• C. $2.52\text{MeV}$
• D. $0.21\text{MeV}$

Answer 1

The correct option is A $4.95\text{MeV}$

The binding energy of ${\text{C}}^{12}$,

$B.E_{C^{12}}=A\times \frac{B.E}{A}$

$\Rightarrow B.E_{C^{12}}=12\times 7.68$

$\Rightarrow B.E_{C^{12}}=92.16\text{MeV}$

The binding energy of ${\text{C}}^{13}$,

$B.E_{C^{13}}=A\times \frac{B.E}{A}$

$\Rightarrow B.E_{C^{13}}=13\times 7.47$

$\Rightarrow B.E_{C^{13}}=97.11\text{MeV}$

Removal of neutron from ${\text{C}}^{13}$ results in ${\text{C}}^{12}$

So, The energy required to remove a neutron from $C^{13}$

$\Delta E=B.E_{C^{13}}-B.E_{C^{12}}$

$\Rightarrow \Delta E=97.11-92.16=4.95\text{MeV}$

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