Question

If we split a nucleus into two smaller nuclei, with a release of energy, has the average binding energy per nucleon increased or decreased?

Short answer

The binding energy per nucleon for smaller nuclei increases due to the split of the nucleus.

Step-by-step solution

Binding energy per Nucleon

The sum of the protons and neutrons in the nucleus is called the nucleons, and it is the same as the mass number of the atom. The energy required to separate each nucleon from the nuclear force of the nucleus is called the binding energy per nucleon. The binding energy per nucleon for an atom is given as:

$E_{bp}=\frac{E_b}{A}$

Here, $E_{bp}$is the binding energy per nucleon, $E_b$ is the binding energy, and A is the mass number of atoms.

Whether average binding energy per nucleon of smaller nuclei increased or decreased

The repulsive force between protons in smaller nuclei becomes less due to the reduced number of protons. In contrast, the nuclear force remains the same, so the overall nuclear force increases and smaller nuclei become more stable than large nuclei. As the nuclear force for smaller nuclei increases, more energy is required to separate the nucleons of smaller nuclei, and binding energy per nucleon for smaller nuclei increases.

We can also see from the formula of binding energy per nucleon that binding energy per nucleon varies inversely with the mass number of nuclei. The mass number of smaller nuclei is small, so the binding energy per nucleon of smaller nuclei becomes more than heavier nuclei.

Therefore, the binding energy per nucleon for smaller nuclei increases due to the split of the nucleus