Calculate the minimum energy required to remove a neutron fr

Calculate the minimum energy required to remove a neutron from the ⁵⁷Fe nucleus.

Solution

The easiest way to calculate the binding energy is to look at the measured mass of the nucleus and the total mass of the constituent nucleons.

E = deltam * c^2

Calcium has 26 protons so mp = 26 * 1.00728u = 26.18928u

31 neutrons so mn = 31 * 1.00866u = 31.26846u

The measured mass of calcium is 56.9353940u
https://en.wikipedia.org/wiki/Isotopes_of_iron

deltam = 26.18928 + 31.26846 - 56.9353940 = 0.522346u

1 u = 931.494 MeV / c^2

E = 0.522346 * 931.494 = 486.5621 MeV is the nuclear binding energy of a Fe-57 nucleus

The binding energy per nucleon is 486.5621 / 57 = 8.536 MeV

At least 8.536 MeV of energy is required to remove a neutron from a Fe-57 nucleus