Free electrons, conduction electrons and the photoelectric effect

Question

I had this statement in my physics textbook

Photoelectric effect is seen only when electrons are bound, because free electrons cannot absorb the whole energy of the photon while conserving momentum and energy.

I found a simple proof for this statement here.

However, the proof states in the beginning itself, that

If the electron is bound to an atom then the atom itself is able to act as a third body repository of energy and momentum

Here's my issue: I've also read that "free electrons" are the loosely bound electrons of an atom, also called the conduction electrons.

If that is the case, then the statement in by book should be wrong, because if the free electrons were to be defined as loosely bound electrons, then it would be possible for them to absorb the whole energy of the photons. In fact, photoelectric effect is generally defined as the emission of the loosely bound electrons from a metal surface when light is incident on it.

On the other hand, though, if we consider that "free electrons" refers to isolated electrons, i.e. when there is no repository in the form of an atom, then the statement seems perfectly fine.

So my question is:

1. Does the definition of "free electron" depend on the context?
2. If yes, then how do we determine which of the definitions is being referred to?

P.S. Wikipedia does say that the definition depends on the context. So the question now boils down to (2) only.

Answer 1

You are asking about free electrons.

Now there are two main cases here:

1. a truly free electron in vacuum

2. an electron in a conductor, that is able to move and create electricity

Now in 1., this truly free electron in a vacuum cannot create the photoelectric effect for you, this electron is only able to emit photons in case it is accelerated by a external magnetic (EM) field.

Now in the case of 2., an electron in a conductor, there are two main opinions on this site:

1. a free electron in a conductor is loosely bound to the valence shells of the atoms

2. a free electron in a conductor is delocalized

This is from wiki:

The photoelectric effect is the emission of electrons or other free carriers when light hits a material. Electrons emitted in this manner can be called photoelectrons.

Now you are asking about the photoelectric effect. In this case, the photons that are interacting with the conductor's surface atoms, need to be of the energy level around the work function of these loosely bound or delocalized electrons. When the photons' energies are about (they need to be close to the work function, it is all about probabilities) the work function of the electrons, this means that they reach the level of energy needed to knock the electron off the atoms' valence shells that they are loosely bound to (we can call them delocalized too).