Question

Why is the binding energy constant between mass numbers $30$ and $170$?

Answer 1

Hint: We have to understand the definition of binding energy first. Then we have to gain some knowledge about the factors on which the binding energy depends and finally we will be able to answer to the question as stated that the binding energy is constant between $30$ and $170$.

Complete answer:
It is stated in the question that the binding energy remains constant between $30$ and $170$. So, now let us found out the reason why the binding energy remains constant between this limit.
We will first understand what binding energy refers to.
Binding energy refers to the amount of energy which is required to separate a particle from a system or to disperse all particles from the system.
Here, the binding energy refers to the nuclear binding energy.
Nuclear binding energy refers to the amount of energy required to separate sub-atomic particles like the proton and neutron from their respective nucleus.
The binding energy is actually a very short range force. So, after a certain limit the force does not have any influence on the atomic particles. Thus, the binding energy becomes constant even if we add any more nucleon. Therefore, the binding energy constant between mass numbers $30$ and $170$.

Note: It must be noted that the binding energy is actually a very short range force. The nuclear force between the nucleons becomes instantly zero when the distance is above a few femtometers. So, as the size of the nucleons increases the distance increases and hence the nuclear force vanishes and hence there is no binding energy.