Binding energy of nucleus - Structure of matter

Question 1

What is the binding energy of a nucleus?

Answer 1

The binding energy of a nucleus determines its stability.

It can be estimated from the total mass defect of the nucleus.

Let us consitder the mass of proton mp and the mass of neutron mn; then the total mass of a nucleus consisting of the protons and neutrons would be given by the sum Zm_p + Nm_n.

However, ,measurements yield the mass of nucleu, m_nucleus lower than the calculated value.

The difference between calculated and measured values is called the mass defect Δm.

Δm = (Z.m_p+ N.m_n) - m_nucleus

Thus a certain part of the rest energy of nucleons, respresented by their rest mass, is converted into the binding energy, which keeps the system together.

The disintergration of the nuclus into individual nucleons would require energy given by

ΔE=mc²

A greater mass deect results in higher binding energy.

Question 2

What is the mass defect of helium?

Answer 2

The binding energy of the nuclus ΔE is related to all of its nucleons.

For example, the mass defect of helium ⁴He is 0.030m.u. that corresponds to the binding energy value of 28 MeV.

Question 3

What is the mass defect of uranium?

Answer 3

The mass defect of uranium ²³⁵U is 1.908m.u.

That corresponds to ΔE = 1741 MeV.

Question 4

Explain the binding energies related to one and various nuclei.

Answer 4

Bining energies related to one nucleon, ΔE/A, are different for various nuclei.

For light and heavy nuclei they amount to 7-7.5 MeV while for nuclei at the muddle of the periodic table of elements they are about 8.5 MeV (see figure on p.20).

Note that binding energies of chemical system (molecules) are of order of several eV, while the above energies are of order of MeV. This means that the nuclei of the elements of middle mass are the most stable.

Question 5

How do nuclear forces contrast to electromagnetic forces.

Answer 5

In contrast to electromagnetic forces, where one charge acts on all the other charges, nuclear forces are saturated, i.e. one nucleon interacts with only one nucleon or with a very low number of other nucleons present in the nucleus.

At low distances, strong interactions are much more stronger as compated with electromagnetic interactions.

Electric charge of nucleus, Ze, forms an electrostatic force field around it with potential U(r) that is a function of the distance r from the nucleus.

Therefore, a potential barrier exists due to the electromagnetic interaction for positively charged particle (proton, deutron, alpha-particle) that enters the nucleus as is demonstrated in the figure 8 in the book, p.20.