Question

H-2 has an atomic mass of 2.013098 u. Calculate its binding energy. Calculate the binding energy per nucleon for H-2.

Answer 1

Part A.

Mass defect is given by:

dm = Mass of Protons in H-2 + mass of neutrons in H-2 + Mass of electrons in H-2 - atomic Mass of H-2

Given that

Atomic mass of H-2 = 2.013098 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 H-2 = 1

Number of neutrons in H-2 = 2 - 1 = 1

Number of electrons in H-2 = 1

So,

dm = 1*mp + 1*mn + 1*me - M_H

dm = 1.007276467 + 1.008664916 + 0.000549 - 2.013098

dm = mass defect = 0.003392383 amu

Binding energy is given by:

E = dm*c^2

c^2 = 931.5 Mev/u

So,

E = (0.003392383 u)*(931.5 MeV/u) = 0.003392383*931.5

E = Binding energy = 3.16 MeV

Part C.

Binding energy per nucleon will be:

BE per nucleon = BE/total number of nucleons

Total number of nucleons = 2

BE per nucleon = BE/total number of nucleons = 3.16/2

Binding energy per nucleon = 1.58 MeV/nucleon

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