Question

What is in the last effects, the nuclear binding energy per atom, and the binding energy per nucleon for U-238? (Isotopic mass of U-238=238.05078 amu)

Answer 1

number of proton = 92

mass of each proton = 1.00727647

so, total mass of proton,

mp = 92 * 1.00727647

mp = 92.669435 amu

number of neutron = 146

mass of each neutron = 1.00866492

so, total mass of neutron,

mn = 146 * 1.00866492

mn = 147.265078 amu

Expected mass of nucleus = mass of protons + mass of neutrons

= 92.669435 + 147.265078

= 239.934514 amu

Actual mass of nucleus = 238.05078 amu

So, mass defect,

Δm = total mass of proton and neutron - actual mass of nucleus

Δm = 239.934514 - 238.05078

Δm = 1.883734 amu

This difference in mass need to be converted to binding energy

dm = 1.883734 u

1 u = 1.6605387E-27 Kg

So,

dm = 1.883734*1.6605387E-27

= 3.128*10^-27 Kg

mass can be converted to energy as given by:

E = m*c^2

so,

E = 3.128*10^-27*(3*10^8)^2 J

E = 2.815*10^-10 J

E = 2.815*10^-10 J

= 2.815*10^-10/(1.602E-19) eV

= 1.757*10^9 eV

E = 1.757*10^9 eV

E 1.757*10^3 MeV

Total Binding energy per atom = 1757 MeV

Number of nucleon = 238

Binding energy per nucleon = 1757/238

= 7.38 MeV/nucleon

Answer:

1757 MeV/atom

7.38 MeV/nucleon