Calculate the average binding energy per nucleon of 5626Fe E

Calculate the average binding energy per nucleon of 56/26Fe. Express your answer using four significant figures. EA = ____MeV/nucleon Calculate the average binding energy per nucleon of 238/92U. Express your answer using four significant figures. EA =____MeV/nucleon

Solution

a) X = Number of protons x 1.007825 x 931.5 MeV

X = 26 x 1.007825 x 931.5 MeV

X = 24408.51 MeV

Y = Number of neutrons x 1.008665 x 931.5 MeV

Y = (56-26) x 1.008665 x 931.5 MeV

Y = 28187.143 MeV

X+Y = energy of protons and neutrons = 24408.51 + 28187.143 =   52595.14

Actual energy = 56.996 x 931.5 = 53091.77 MeV

BE = X+Y - Actual energy = 496.63 MeV

BE per nucleon = BE / (56 ) = 496.63/56 = 8.86 MeV

b) X = Number of protons x 1.007825 x 931.5 MeV

X = 92 x 1.007825 x 931.5 MeV

X = 86368.586 MeV

Y = Number of neutrons x 1.008665 x 931.5 MeV

Y = (238-92) x 1.008665 x 931.5 MeV

Y = 137177.431 MeV

X+Y = 137177.431 + 86368.586 =  223546.01

Actual energy = 232.03588 x 931.5 = 216141.42 MeV

BE = X+Y - Actual energy = 223546.01 -   216141.42 = 7404.59 MeV

BE per nucleon = BE / (238) = 31.111 MeV