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Standard XII
Physics
Binding Energy
Which of the ...
Question

Which of the following represents the binding energy of a nucleus:

A
The average energy of each nucleon
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B
The energy needed to split the nucleus into its parts
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C
The mass-energy difference between protons and neutrons
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D
The energy necessary to overcome the neutron-neutron repulsion
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E
The energy required to remove a proton from the nucleu
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Solution

The correct option is B The energy needed to split the nucleus into its parts
It is observed that mass of a stable nucleus is always less than the total mass of constituent nucleons.This difference of mass is known as mass defect. When a nucleus is formed from the free nucleons mass defect is released in the form of energy by Einstein's mass-energy relation. This energy is used to bind the nucleons to form a nucleus therefore an equivalent amount of energy is required to split the nucleus into its parts, that is called binding energy of nucleus.

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Q. Calculate the minimum energy needed to separate a neutron from a nucleus with Z protons and N neutrons it terms of the masses MZ.N' MZ,N−1 and the mass of the neutron.
Q.

Show that the minimum energy needed to separate a proton from a nucleus with Z protons and N neutrons is △E=(Mz−1,N+MH−MZ,n)C2 Where MZ,n= mass of an atom with Z protons and N neutrons in the nucleus and MH= mass of a hydrogen atom. This energy is known as proton-separation energy.

Q. The masses of neutron and proton are 1.0087 and 1.0073 amu respectively. If the neutrons and protons combine to form a Helium nucleus of mass 4.0015amu, the binding energy of the Helium nucleus will be :
Q. Nuclear binding energy is the energy released during the hypothetical formation of the nucleus by the condensation of individual nucleons. Thus, binding energy per nucleon =Total binding energyNumber of nucleons For example, the mass of hydrogen atom is equal to the sum of the masses of a proton and an electron. For other atoms, the atomic mass is less than the sum of the masses of protons, neutrons and electrons present. This difference in mass, termed as mass defect, is a measure of the binding energy of protons and neutrons in the nucleus. The mass-energy relationship postulated by Einstein is expressed as:
ΔE=Δmc2
Where ΔE is the energy liberated, Δm is the loss of mass, and c is the speed of light.

MP and Mn are masses of a proton and a neutron respectively. For a nucleus, its binding energy is B and it contains Z protons and N neutrons, the correct relation for this nucleus if C is velocity of light is:
Q. Calculate the binding energy and binding energy per nucleon (in MeV) of a nitrogen nucleus (147N) from the following data :
Mass of proton = 1.00783 u
Mass of neutron = 1.00867 u
Mass of nitrogen nucleus = 14.00307 u
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