Answer :
To solve this question,
let us first calculate how much all the nucleons will weigh when they are apart,
that is:
Mass of 25 protons = 25(1.0073) = 25.1825 amu
Mass of neutrons = (55-25)(1.0087) = 30.261 amu
So, total mass of nucleons = 30.261+25.1825 =
55.4435 amu
Now we subtract the mass of nucleons and mass of the Mn
nucleus:
55.4435 - 54.938 = 0.5055 amu
This difference in mass is what we call as the mass defect of
a nucleus. Now we calculate the binding energy using the formula:
E=mc^2
But first convert mass defect in units of SI (kg):
Δm = 0.5055 amu = (0.5055) / (6.022x10^26)
Δm = 8.3942x10^-28 kg
Now applying the formula,
E=Δm c^2
E=(8.3942x10^-28)(3x10^8)^2
E=7.55x10^-11 J
Convert energy from Joules to mev then divide by total number of nucleons (55):
E = 7.55x10^-11 J * (6.242x10^12 mev / 1 J) / 55 nucleons
E = 8.57 mev / nucleon