Calculate the average binding energy per nucleon of each of the following isotop

Question

Calculate the average binding energy per nucleon of each of the following isotopes. (a) 52 24 Cr Incorrect: Your answer is incorrect. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. MeV/nucleon (b) 234 91 Pa Incorrect: Your answer is incorrect. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. MeV/nucleon

Explanation / Answer

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

X = 24 x 1.007825 x 931.5 MeV

X = 22530.9357 MeV

Y = Number of neutrons x 1.008665 x 931.5 MeV

Y = (52-24) x 1.008665 x 931.5 MeV

Y = 26308 MeV

X+Y = energy of protons and neutrons = 48838.936

Actual energy = 51.996 x 931.5 = 48434.274 MeV

BE = X+Y - Actual energy = 404.662 MeV

BE per nucleon = BE / (24+28) = 7.78 MeV

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

X = 91 x 1.007825 x 931.5 MeV

X = 85429.79 MeV

Y = Number of neutrons x 1.008665 x 931.5 MeV

Y = (234-91) x 1.008665 x 931.5 MeV

Y = 134357.38 MeV

X+Y = 219788.5

Actual energy = 231.03588 x 931.5 = 215209.922 MeV

BE = X+Y - Actual energy = 4577.252 MeV

BE per nucleon = BE / (234) = 19.56 MeV

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