Binding energy of an atom

Question

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

Answer 1

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.

Answer 2

The binding energy of the nucleus is an energy (or equivalent mass via $c^2$) which in some sense accounts for the "extra" (or lacking) energy which is not accounted for by the mass of its constituent particles. The binding energy per nucleon is exactly what it says, the binding energy divided by the number of nucleons (a nucleon is a proton or a neutron).

Answer 3

Yes there is difference between binding energy of atom and nucleus. Rest mass energy of atom=rest mass energy of electron +rest mass energy of nucleus - Binding energy of the atom. Rest mass energy of nucleus =rest mass of proton +rest mass energy of neutrons - Binding energy of nucleus.

Since both atom and nucleus are bounded system because of attraction forces (nuclear force in atom and coulombic force in atom). So some energy are required to brake them speartaly in both case.

Binding energy of atom is very small (in eV) compared to binding energy of nucleus (in MeV).

Answer 4

binding energy per nucleon means the nuclear energy between nucleons to attract each other.whereas binding energy of atoms is the bond energy of atoms to react with others.