Question

Einstein showed what could be explained if photons carried quantized amounts of energy?

Answer 1

The photoelectric effect (the spontaneous emission of electrons when illuminated by light of a sufficiently high frequency.)

Explanation:

This phenomenon was known, but not understood, until Einstein’s paper in 1905 (his “marvellous year”) and contributed to the ultra-violet catastrophe being resolved (see here: https://en.m.wikipedia.org/wiki/Ultraviolet_catastrophe#Solution)

It predicted that photoelectrons would only be emitted from a negatively charged plate when the energy (given by `E = h.f`) exceeded the work function (`phi`) of that particular metal. More details (perhaps more than you want) here: https://physics.info/photoelectric/

This was the very start of the most accurate and successful theory ever known in Physics - Quantum Theory. Entertainingly, a recent conference of physicists working in the field was questioned as to their understanding of Quantum Theory (n=129) just over 1/3 favoured the Copenhagen interpretation, slightly fewer believed the Many Worlds Hypothesis, but almost a third we’re happy to confess that they did not really understand it sufficiently to form an opinion.

I like the fact that we are all still learning!