Separation energy formula E = \Delta m c^2 where, \Delta m mass defect and c - speed of light

Step 1: Determine the energy required to separate the neutron from the nucleus ^{41}_{20} Ca

Nuclear reaction for Calcium

^{41}_{20} Ca \rightarrow ^{40}_{20} Ca + ^{1}_{0} n

Mass defect \Delta m = \text{ mass of } ^{40}_{20} Ca + \text{ mass of } ^{1}_{0} n - \text{ mass of } ^{40}_{20} Ca

Given that

m (^{40}_{20} Ca) = 39.962591 u

m (^{41}_{20} Ca) = 40.962278 u

m (^{1}_{0} n) = 1.008665

\Delta m = 39.962591 + 1.008665 - 40.962278

\Delta m = 0.008978 u

Separation energy E = \Delta m c^2 = 0.008978 c^2

E = 0.008978 c^2 * 931.5 MeV/c^2

E = 8.363007 MeV

Hence, energy required to separate the neutron E = 8.363007 MeV

Step 2: Determine the energy required to separate the neutron from the nucleus ^{27}_{13} Al

Nuclear reaction for Aluminium

^{27}_{13} Al \rightarrow ^{26}_{13} AI + ^{1}_{0} n

Mass defect \Delta m = \text{ mass of } ^{26}_{13} Al + \text{ mass of } ^{1}_{0} n - \text{ mass of } ^{27}_{13} Al

Given masses

m (^{26}_{13} Al) = 25.986895 u

m (^{27}_{13} Al) = 26.981541 u

\Delta m = 25.986895 + 1.008665 - 26.981541

\Delta m = 0.0140190

Separation energy E = \Delta m c^2 = 0.0140190 c^2

E = 0.0140190 c^2 * 931.5 MeV/c^2

E = 13.059 MeV

Thus, energy required to separate the neutron E = 13.059 MeV