Question 36: Atoms & Nuclei

Question

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

Accepted Answer

To determine the energy required to remove a neutron from $$\mathrm{C}^{13}$$, we need to find the difference in total binding energy between $$\mathrm{C}^{13}$$ and $$\mathrm{C}^{12}$$.
The binding energy per nucleon for $$\mathrm{C}^{13}$$ is given as $$7.47 \mathrm{~MeV}$$. Since $$\mathrm{C}^{13}$$ has 13 nucleons, its total binding energy is:
$$ E_{B,\mathrm{C}^{13}} = 7.47 \mathrm{~MeV} 	imes 13 $$
$$ E_{B,\mathrm{C}^{13}} = 97.11 \mathrm{~MeV} $$
The binding energy per nucleon for $$\mathrm{C}^{12}$$ is given as $$7.68 \mathrm{~MeV}$$. Since $$\mathrm{C}^{12}$$ has 12 nucleons, its total binding energy is:
$$ E_{B,\mathrm{C}^{12}} = 7.68 \mathrm{~MeV} 	imes 12 $$
$$ E_{B,\mathrm{C}^{12}} = 92.16 \mathrm{~MeV} $$
The energy required to remove a neutron from $$\mathrm{C}^{13}$$ is the difference between the total binding energy of $$\mathrm{C}^{13}$$ and $$\mathrm{C}^{12}$$:
$$ E_{	ext{remove}} = E_{B,\mathrm{C}^{13}} - E_{B,\mathrm{C}^{12}} $$
$$ E_{	ext{remove}} = 97.11 \mathrm{~MeV} - 92.16 \mathrm{~MeV} $$
$$ E_{	ext{remove}} = 4.95 \mathrm{~MeV} $$
Now, let's convert this energy from MeV to Joules. Since 1 MeV is equivalent to $$1.60218 	imes 10^{-13} \mathrm{~J}$$:
$$ E_{	ext{remove}} = 4.95 \mathrm{~MeV} 	imes 1.60218 	imes 10^{-13} \mathrm{~J/MeV} $$
$$ E_{	ext{remove}} = 7.92 	imes 10^{-13} \mathrm{~J} $$
Therefore, the energy required to remove a neutron from $$\mathrm{C}^{13}$$ is $$7.92 	imes 10^{-13} \mathrm{~J}$$. The correct option is:
Option C:
$$7.92 	imes 10^{-13} \mathrm{~J}$$

Answer

$$7.92 	imes 10^{-13} \mathrm{~MeV}$$

Answer

$$4.95 	imes 10^{-13} \mathrm{eV}$$

Answer

$$7.92 	imes 10^{-13} \mathrm{~J}$$

Answer

$$7.92 	imes 10^{-19} \mathrm{~J}$$

Atoms & Nuclei

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

Choose the correct answer: