Question

A) Calculate the mass defect of the oxygen nucleus 16  8O. The mass of neutral 16  8O is equal to 15.994914 atomic mass units. Answer in amu.

B) Calculate the binding energy E of the oxygen nucleus 16  8O (1eV=1.602×10−19J). Answer in MeV

C) Calculate the binding energy per nucleon of the oxygen nucleus 16  8O. Answer in MeV / nucleon

Answer 1

A)

mass defect = number of protons * mass of one proton + number of neutrons * mass of one neutron - mass of the nucleus

Atomic number of Oxygen = 8 (number of protons = atomic number)

mass of 1 proton = 1.00728 amu

Atomic number of Oxygen = 16 ( number of neutrons = atomic mass - atomic number = 16 - 8 = 8)

mass of 1 neutron ~ 1.0088665 amu.

mass of the oxygen nucleus = 15.994914

substituting the values, we have;

mass defect = 8*1.00728 + 8*1.0088665-15.994914 = 0.13706 amu

B)

as shown above, the sum of masses of the oxygen-16 nucleus = 8*(1.00728 amu) + 8*(1.0088665 amu) = 16.12756 amu

The difference between the observed mass and the sum of masses of isolated nucleons is equal to binding energy of the nucleus ( it is same as the mass defect but with a negative sign, according to the conventions used, indicating more stability as a collection of isolated particle since its energy is less than that of isolated protons and neutrons)

therefore,
Binding Energy = (15.9905 - 16.12756) amu = - 0.13706 amu

Since, 1eV=1.602×10⁻¹⁹ J

1.602×10⁻¹³J = 1 MeV

and 1 amu = 931 MeV
0.13706 amu * 931 MeV/amu = 127.6 MeV

C)

As there are 16 nucleons in Oxygen-16, binding energy per nucleon = -127.6 MeV/ 16 nucleons = -7.975 MeV/nucleon