For the nuclei 11_5 B and 11_6 C, determine the difference in binding energy per

Question

For the nuclei 11_5 B and 11_6 C, determine the difference in binding energy per nucleon (in MeV). (Let the mass of a proton be 1.0078 u, the mass of a neutron be 1.0087 u, the mass of 11_5 B be 11.0093 u, and the mass of 11_6 C be 11.0114 u.) This difference in binding energy is due to which of the following? Greater electron attraction for the 11_6 C atom Greater proton repulsion for the 11_6 C nucleus Greater neutron attraction for the 11_6 C nucleus Greater electron repulsion for the 11_6 C atom Greater proton attraction for the 11_6 C nucleus Greater neutron repulsion for the 11_6 C nucleus

Explanation / Answer

Mass of 5B11 = 11.0093

Mass of 6C11   = 11.0114

Mass of proton = 1.0078 u

Mass of neutron = 1.0087 u

(Mass of 5 protons + Mass of 6 neutrons) for 5B11

                                                 = 5 x 1.0078 + 6 x 1.0087 = 11.0912 u

(Mass of 6 protons + Mass of 5 neutrons) for 5B11

                                                 = 6 x 1.0078 + 5 x 1.0087 = 11.0903 u

Difference between masses for 5B11 = 11.0093 - 11.0912

                                                   = -0.0819 = 0.0819*931 = 76.24 MeV

Difference between masses for 6B11 = 11.0114 - 11.0903

                                                   = -0.0789 = 0.0789*931 = 73.45 MeV

Difference in Binding Energies = 2.79 MeV

The difference in binding energies is due to greater neutron repulsion for 6C11 nucleus

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