Question

Constants:       1 u = 1.66054 x 10^-27 kg

                                Electron rest mass = 9.10939 x 10^-31 kg

                        Proton rest mass = 1.67262 x 10^-27 kg

                        Neutron rest mass = 1.67493 x 10^-27 kg

                        Speed of light = 2.998 x 10⁸ m/s

                        Avogadro’s number = 6.02 x 10²

Calculate the nuclear binding energy in Joules of one Mo⁹⁶₄₂nucleus? What is the nuclear biding energy of a mole of Mo⁹⁶₄₂ atoms? What is the energy per nucleon? The observed atomic mass is 95.9046785 u.

Answer 1

Calcualtion of energy of 1 amu using E=mc²

1 amu x c² = 1.66054 x 10^-27 kg x (2.998 x 10⁸ m/s) = 931.49432 MeV

Number of protons - 42

Number of neutrons - 54

Total number of nucleons = 96

Total mass of protons: 42 x 1.67262 x 10^-27 kg =70.25004 x 10^-27 kg

Total mass of neutrons: 54 x1.67493 x 10^-27 kg = 90.44622 x 10^-27kg

Total mass: 160.69626 x 10^-27 kg

In terms of amu: 160.69626 x 10^-27 kg/1.66054 x 10^-27 kg amu^-1 = 96.773495 amu

Observed atomic mass: 95.9046785 u.

Mass defect:96.773495 amu -95.9046785 u = 0.8688168 amu

Binding erergy = 0.8688168 amu x 931.49432 MeV /amu = 809.29 MeV/per atom

1 MeV = 1.602177x10^-13 J

In joules: 809.29 x 1.602177x10^-13 J = 1296.6258 x 10^-13J = 129.66258 pJ (picojoules)

For one mole of Mo nuclei = 809.29 x 1.602177x10^-13 x 6.02 x 10²³ = 7.80568 x 10¹⁰ J

The energy per nucleon is 809.29 MeV/96 = 8.430 MeV = 8.430 x 1.602177x10^-13 J = 1.35065 pJ