Question

When the number of nucleons in a nucleus increases, the binding energy per nucleon :

• A. increases continuously with mass number
• B. decreases continuously with mass number
• C. remains constant with mass number
• D. first increases and then decreases with increase in mass number

Answer 1

The correct option is D first increases and then decreases with increase in mass number

The binding energy is the energy released when a nucleus is assembled from its constituent nucleons. It is thus a measure of the amount of energy held within the bonds of the atom and corresponds to the energy required to be put in again to pull the nucleons apart. Hence, the energy equivalent of the mass-defect is called the binding-energy of the nucleus.

The larger the nucleus, the greater is the internal repulsive forces due to the greater number of protons and less energy must be applied to remove a nucleon from the nucleus, hence the binding energy is lower. The greater the binding energy, the more stable the atom is.

This variation in the binding energy per nucleon ($\frac{BE}{A}$) is easily seen when the average $\frac{BE}{A}$ is plotted versus atomic mass number (A), as shown in the figure, as the atomic mass number increases i.e. the number of particles in a nucleus increases, the total binding energy also increases first and then decreases for A > 56.