Calculate the mass defect and nuclear binding energy per nucleon of the each of

Question

Calculate the mass defect and nuclear binding energy per nucleon of the each of the nuclides indicated below.

Part A O-16 (atomic mass = 15.994915 amu) Express your answer using five decimal places. Mass defect = amu S

Part B Express your answer using four significant figures. Binding energy per nucleon = MeV/nucleon

Part C Ni-58 (atomic mass = 57.935346 amu) Express your answer using five decimal places. Mass defect = amu

Part D Express your answer using four significant figures. Binding energy per nucleon = MeV/nucleon

Part E S-32 (atomic mass = 31.97207 amu) Express your answer using five decimal places. Mass defect = amu Part F

Express your answer using four significant figures. Binding energy per nucleon = MeV/nucleon

Explanation / Answer

Part A O-16 (atomic mass = 15.994915 amu) Express your answer using five decimal places. Mass defect = amu S

Mass defect = m x c2

where c = speed of light

m = Neme + Nnmn + Npmp - M

M= atomic mass, Ne = no. of electrons in one atom, Np = no. of protons, Nn = no. of nuetrons and Me, Mp, Mn their respective masses.

electron mass = 0.000548579867 atomic mass units

proton mass = 1.00727638 atomic mass units

neutron mass = 1.0086654 amu

find in amu m = 8 x  0.000548579867 + 8 x 1.00727638 + 8 x1.0086654 - 15.994915 = 0.13700 amu

Mass defect = m = 0.13700 amu

Part B Express your answer using four significant figures. Binding energy per nucleon = MeV/nucleon

Binding energy = m x c2 = m (in amu) x 931.6 MeV =127.6359 MeV

Binding energy per nucleon = (Binding energy) /(Np + Nn) = 127.6359/16 =7.97724 MeV/nucleon

Part C Ni-58 (atomic mass = 57.935346 amu) Express your answer using five decimal places. Mass defect = amu

mass of Ni-58 = 57.935346 amu
number of protons = 28
mass of protons in Ni = 28 * 1.00728 = 28.20384
mass of neutrons = (58 - 28) * 1.00866 = 30.2598
total mass of nucleons = 28.20384 + 30.2598 = 58.46364
mass defect (dm)= 58.46364 - 57.935346 = 0.528294

Part D Express your answer using four significant figures. Binding energy per nucleon = MeV/nucleon

binding energy = dm * 931.5 MeV
               = 0.528294 * 931.5
               = 492.106 MeV
Binding energy per nucleon = 492.106/58 = 8.4846 MeV

Part E S-32 (atomic mass = 31.97207 amu) Express your answer using five decimal places. Mass defect = amu

Similar calculations for Sulphur with Ne = Np = Nn = 16

m = 0.291774 amu

Part F

Express your answer using four significant figures. Binding energy per nucleon = MeV/nucleon

BE = 271.8171

BE/nucleon = BE/32 = 8.49428 Mev/nucleon

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