In the per particle view, a given density is shared by \(Z\) particles.
In the per atom view, a given density has \(Z\) particles.
In the per particle view, the whole atom is moving (with a given \(KE\)) and carries with it \(Z\) particles.
In the per atom view, the atom is bombarded with photons, each atom has \(Z\) particles that can interact with the photons.
In,
\(E_{input\,atom}=E_{photon}=...density*Z...\)
photons interacts with an atom with \(Z\) particles. More energy is needed to interact with an atom, where \(Z\) particle coalesce into one as a quasi-nucleus. The atom is stationary, photons move and collide with it.
In,
\(E_{input\,particle}=E_{particle}=...\cfrac{density}{Z}...\)
particles interacts with particles. Less energy is needed to interact at individual particle level compared to the interaction with a quasi-nucleus. Relatively, the atom is moving in space with \(Z\) number of particles. A gas.
Maybe in a solid, we should have taken the per atom perspective too. In this case free particles move within the confines of the solid.
Good morning!
