Question

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

• A. \(7.92 \times 10^{-13} \, \text{MeV}\)
• B. \(4.95 \times 10^{-13} \, \text{eV}\)
• C. \(7.92 \times 10^{-13} \, \text{J}\)
• D. \(7.92 \times 10^{-19} \, \text{J}\)

Hint:

When converting from MeV to Joules, remember that \(1 \, \text{MeV} = 1.602 \times 10^{-13} \, \text{J}\).

Answer 1

The Correct Option is C

The energy required to remove a neutron from the nucleus is equivalent to the difference in the binding energy per nucleon of \(^{13}C\) and \(^{12}C\), since removing a neutron will effectively decrease the number of nucleons in the nucleus. The energy difference is given by: \[ E_{\text{diff}} = (7.68 - 7.47) \, \text{MeV} = 0.21 \, \text{MeV} \] Now, to find the energy required to remove a neutron from \(^{13}C\), we calculate the energy in joules using the relation: \[ 1 \, \text{MeV} = 1.602 \times 10^{-13} \, \text{J} \]
Thus, the energy required is: \[ E_{\text{diff}} = 0.21 \, \text{MeV} \times 1.602 \times 10^{-13} \, \text{J/MeV} = 7.92 \times 10^{-13} \, \text{J} \]
Thus, the energy required to remove a neutron from \(^{13}C\) is \(7.92 \times 10^{-13} \, \text{J}\).