Question

The mass of the nuclide 16/8O is 15.995u .

A) What is the total binding energy for this nucleus?

Eb =     MeV  

B) Determine its average binding energy per nucleon.

Eb/A= Mev/nucleon

Answer 1

Binding Energy per nucleon = Binding energy / total no. of nucleons

Binding energy BE = mass defect * c²

mass defect = (difference in sum of masses of no of protons and neutrons present and mass of nucleus)

We use masses in atomic mass units (u)

Proton mass : m_p: 1.0073 u

Neutron mass: m_n : 1.0087 u

1 u = 1.66 * 10^-27 kg = 931.5 MeV/c²

First we need to calculate mass defects for the given nuclei, then calculate BE using above formula and finally find BE per nucleon. (To find mass of the given nucleus you need to consult book/internet).

16O 8

No. of nucleons: 16

No. of protons: 8

Total mass of protons: 8 m_p = 8 * 1.0073= 8.0584 u

No. of neutrons: 8

Total mass of neutrons: 8 m_n = 8 * 1.0087 = 8.067 u

Mass of the 16 O (given): 15.995 u (I am assuming this is atomic mass not nucleus mass as ques says)

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No. of electrons: 8

Mass of the nucleus: Mass of 16 O atom - Mass of 8 electrons

Mass of 1 electron: 0.000548u

Mass of 8 electrons = 0.00438 u

Mass of 16 O nucleus: 15.995 - 0.00438=15.9906 u

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mass defect: (8.0584 + 8.067 - 15.9906) = 0.1348 u

convert mass units from u to MeV/c²

mass defect: 0.1348 u = 0.1348 * 931.5 MeV/c² = 125.6 MeV/c²

BE: mass defect * c² = 125.6 MeV

BE/nucleon: 125.6/16 = 7.847 = 7.847 MeV/nucleon