Question

Calculate the nuclear binding energy for 5525mn in megaelectronvolts per nucleon (mev/nucleon).

Answer 1

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