The atomic mass of C-12 (\( {}^{12}_{6}C \)) is 12.000000 u and that of C-13 (\( {}^{13}_{6}C \)) is 13.003354 u. The energy required to remove a neutron from C-13 (\( {}^{13}_{6}C \)) 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) → \( 4.94\,\mathrm{MeV} \)
Removing a neutron changes \( {}^{13}_{6}C \) into \( {}^{12}_{6}C \) plus a free neutron. The energy needed is the neutron separation energy, equal to the mass difference of the products and the original nucleus, converted to energy.
\( \displaystyle {}^{13}_{6}C \rightarrow {}^{12}_{6}C + {}^{1}_{0}n \)
Atomic masses can be used directly, because both sides contain the same number of electrons (six) and their masses cancel.
\( \displaystyle \Delta m = m({}^{12}_{6}C) + m_n - m({}^{13}_{6}C) = 12.000000 + 1.008665 - 13.003354 = 0.005311\,\mathrm{u} \)
\( \displaystyle E = \Delta m \times 931\,\mathrm{MeV\,u^{-1}} = 0.005311 \times 931 = 4.94\,\mathrm{MeV} \)