Note: Give answers to 4 significant figures for m , and give answers to 3 signif

Question

Note: Give answers to 4 significant figures for m, and give answers to 3 significant figures for Eb / A.

Nucleus Z (A Z) m (in u) m (in u) Eb / A (in MeV) 55 25 Mn 54.938048 56 26 Fe 55.934940 59 27 Co 58.933198 The region of greatest binding energy per nucleon Nuclei to the right of is shown by the tan band. 2008 Pb are unstable. 12 He Ne Pb 226. Mo Ra 127 Na 107 Ag 56, 14 The curve represents the binding energy for 11 the most stable isotopes. 20 40 660 80 100 120 140 160 180 200 220 240 Mass number A

Explanation / Answer

For Mn:,number of protons = 25, number of neutrons = 55-25 = 30. So, the binding energy is:

B = (25x1.007276 u + 30x1.008665 u - 54.938048u)c2 = (0.503802u)c2 = (0.503802)x931.5MeV = 469.29 MeV

m = 0.503802u

Binding energy per nucleon = 469.29 MeV/55 = 8.532MeV

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For Fe:,number of protons = 26, number of neutrons = 56-26 = 30. So, the binding energy is:

B = (26x1.007276 u + 30x1.008665 u - 55.934940u)c2 = (0.514186u)c2 = (0.514186)x931.5MeV = 478.964MeV

m = 0.514186u

Binding energy per nucleon = 478.964MeV/56 = 8.552MeV

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For Co:,number of protons = 27, number of neutrons = 59-27 = 32. So, the binding energy is:

B = (27x1.007276 u + 32x1.008665 u - 58.933198u)c2 = (0.540534u)c2 = 0.540534x931.5MeV = 503.507MeV

m = 0.540534u

Binding energy per nucleon = 503.507MeV/59 = 8.534MeV

Thus it's clear that Fe has the highest binding energy per nucleon among the three.

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