Question

Determine the binding energy (in MeV) per nucleon for the nuclides: a) 816O, b) 817O, c) 2656Fe, d) 92235U

please show steps!

Answer 1

Answer – a) ¹⁶₈O

We know exact mass of O = 15.9949 amu

In the ¹⁶₈O there are 8 protons and , 16-8 = 8 neutrons

Mass of neutron =1.008665 amu
mass of proton = 1.007825 amu

So mass of ¹⁶₈O = (8*1.007825) + (8*1.008665)

                               = 16.1319 amu

So mass defec, Δm = 16.1319 amu - 15.9949 amu

                                 = 0.1370 amu

We know,

Energy = Δm *931.494 MeV/amu

             = 0.1370 amu* 931.494 MeV/amu

             = 127.63 MeV

Binding energy in MeV per nucleons =127.63 MeV /16 nucleons

                                                       = 7.98 MeV/nucleons

b) ¹⁷₈O

mass of ¹⁷₈O = (8*1.007825) + (9*1.008665)

                      = 17.1406 amu

So mass defec, Δm = 17.1406 amu – 16.9991 amu

                                 = 0.1415 amu

We know,

Energy = Δm *931.494 MeV/amu

             = 0.1415 amu* 931.494 MeV/amu

             = 131.8 MeV

Binding energy in MeV per nucleons =131.8 MeV /17 nucleons

                                                       = 7.75 MeV/nucleons

c) ⁵⁶₂₆Fe

mass of ⁵⁶₂₆Fe = (26*1.007825) + (30*1.008665)

                      = 56.4634 amu

So mass defec, Δm = 56.4634 amu – 55.9349 amu

                                 = 0.5285 amu

We know,

Energy = Δm *931.494 MeV/amu

             = 0.5285 amu* 931.494 MeV/amu

             = 492.29 MeV

Binding energy in MeV per nucleons =492.29 MeV /56 nucleons

                                                     = 8.79 MeV/nucleons

d) ²³⁵₉₂U

mass of ²³⁵₉₂U = (92*1.007825) + (143*1.008665)

                       = 236.9589 amu

So mass defec, Δm = 236.9589 amu – 235.0439 amu

                                 = 1.91 amu

We know,

Energy = Δm *931.494 MeV/amu

             = 1.91amu* 931.494 MeV/amu

             = 1783.9 MeV

Binding energy in MeV per nucleons =17839 MeV /235 nucleons

                                                       = 7.59 MeV/nucleons