Question

Careful measurements of the mass of a gold-197 nucleus yield a value of 196.967 u. Compute the binding energy in MeV and the binding energy per nucleon for this nuclide.

MeV?

MeV/nucleon?

Answer 1

1.

Mass defect is given by:

dm = Mass of Protons in gold+ mass of neutrons in gold+ Mass of electrons in gold- atomic Mass of gold

Given that

Atomic mass of gold = 196.96657 u

Mass of 1 proton = 1.007276467 u

Mass of 1 electron = 9.11*10^-31 kg = 0.000549 amu

Mass of 1 neutron = 1.008664916 u

Number of protons in gold = 79

Number of neutrons in gold = 197 - 79 = 118

Number of electrons in gold = 79

So,
dm = 79*mp + 118*mn + 79*me - M_Au

dm = 79*1.007276467 + 118*1.008664916 + 79*0.000549 - 196.96657

(1 amu = 1.6605*10^-27 kg)

dm = mass defect = 1.67410198 amu = 2.779846*10^-27 kg

Binding energy is given by:

E = dm*c^2

c^2 = 931.5 Mev/u

So,

E = (1.67410198 u)*(931.5 MeV/u) = 1.67410198*931.5

E = Binding energy = 1559.42599437 MeV

E = Binding energy = 1559.43 MeV

Binding energy per nucleon will be:

BE per nucleon = BE/total number of nucleons

Total number of nucleons = 197

BE per nucleon = BE/total number of nucleons = 1559.42599437/197

Binding energy per nucleon = 7.92 MeV/nucleon

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