The atomic mass of ${^{12}_{6}C}$ is 12.000000 u and that of ${^{13}_{6}C}$ is 13.003354 u. The energy required to remove a neutron from ${^{12}_{6}C}$ is
(Given: Mass of neutron is 1.008665u and 1 u = 931 MeV)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4.94 MeV
Given:
Mass of $^{12}_6\text{C} = 12.000000\,\text{u}$
Mass of $^{13}_6\text{C} = 13.003354\,\text{u}$
Mass of neutron: $m_n = 1.008665\,\text{u}$
Conversion: $1\,\text{u} = 931\,\text{MeV}$
Energy required to remove a neutron from $^{13}_6\text{C}$:
Neutron separation energy $S_n = [m(^{12}\text{C}) + m_n - m(^{13}\text{C})] c^2$
$S_n = (12.000000 + 1.008665 - 13.003354)\,\text{u} \cdot 931\,\text{MeV/u}$
$S_n = (13.008665 - 13.003354)\,\text{u} \cdot 931 = 0.005311 \cdot 931 \approx 4.94\,\text{MeV}$
Answer: $S_n \approx 4.94\,\text{MeV}$