Does every photon liberate an electron?

The simple answer is “no” but there are many reasons to consider. Assuming the radiation is above the threshold frequency, there are still other issues affecting the release of electrons. The fact that photons can easily pass between or even through atoms without hitting (interacting with) an electron gives rise to a variety of possibilities:

1. The photon strikes an electron near the surface of the metal. The electron uses the energy that it has gained to leave the atom and head off to freedom. That’s an easy one.

2. The photon hits an electron near the surface of the metal. The electron leaves the atom but heads off deeper into the metal and never manages to escape.

3. The photon passes deep into the metal before it hits an electron. The electron leaves the atom and heads towards the surface and escapes!

4. The photon passes deep into the metal before it hits an electron. The electron leaves the atom and heads towards the surface but it doesn’t have enough energy to push its way past all the other atoms to get to the surface so it comes to rest inside the metal and never escapes.

5. The photon passes deep into the metal before it hits an electron. The electron leaves the atom and heads off in the wrong direction and never escapes.

So in fact a very small proportion of the photons that arrive at the metal will cause photoelectrons to be emitted.

Theory
Einstein's Solution
Photons

Glossary

A single photon is very small so it hits just one electron and has sufficient energy to knock it out of the metal.