I would like to know if there is any difference between the binding energy of a nucleus and the binding energy of an atom and what exactly do we mean when we say Binding energy per nucleon..
Edit to the Comment below: So I am currently studying a course in Nuclear physics and the concept of Binding energy comes up when we are discussing ways of calculating the charge and matter distribution inside the nucleus. So, we use scattering experiments to work out the distribution of protons and neutrons inside the nucleus and based on that we defined the binding energy of an atom to be the mass deficit multiplied by $c^2$. But then later on when we were deriving the semi empirical mass formula we suddenly started called $M(Z,A)$ as the binding energy of the nucleus which is why I was wondering what the difference was. And with regards to the binding energy per nucleon, I wanted to know whether the binding energy per nucleon is the same as binding energy of the nucleus or not
Best Answer
Yes. Usually 'binding energy' is only used for nuclei, but in the context of atoms it would be intended as the (first) ionisation energy - i.e. the energy required to strip the outermost electron, making it an ion. When dealing with the Hydrogen atom, for example, its mass ($m_H$) is given by $m_{nucleus} + m_{electron} - \frac{E}{c^2}$ where $E$ is the energy you get from solving the Schrödinger equation. You can see that $E$ can be thought as the binding energy between the nucleus and the electron, in analogy with the semi-empirical mass formula for nuclei.
The binding energy per nucleon is the binding energy of the nucleus divided by the number of nucleons. This tells you approximately how much each nucleon is contributing to the stability of the whole nucleus. If you were to remove one, you know how much less stable the nucleus would be. Once you remove one, the BEpN would actually change, but you can still approximate it by the previous value.