Question

In: Physics

If a nucleus has mass M, Z protons (mass mp) and N neutrons (mass mn) its...

If a nucleus has mass M, Z protons (mass mp) and N neutrons (mass mn) its binding energy is equal to

Expert Solution

Binding energy:- It is the minimum energy required to separate nucleons (protons and neutrons) inside the nucleus. It also shows that how strongly the nucleons bind together inside the nucleus of an atom.

Let,

: be the binding energy of the nucleus.

As given:-

: is the mass of the nucleus.
: is the number of protons.
: is the number of neutrons.
: is mass of the proton.
: is mass of the neutron.

The nucleus of an atom is consists of protons and neutrons. But the sum of the masses of the protons and neutrons is not equal to the mass of the nucleus. The nuclear mass (M) is always less than the sum of the masses of the protons and neutrons. This happens due to strong interactions between protons and neutrons. This decrease in mass of the system is known as the mass defect.

Thus the mass defect is defined by ,

Now, according to the mass-energy equivalence relation we have,

Where, c is the speed of light.

From this relation we can have the binding energy of the nucleus as,

This relation will gives us the binding energy of the nucleus.

After conversion of atomic mass unit to kilogram,

Therefore the binding energy is given as,

genius_generous answered 4 months ago

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