CBSE Class 12 · 2019 · Modern PhysicsShort Answer

The wave theory fails on three counts: it predicts (i) emission for any frequency if the intensity is large enough (no threshold frequency), (ii) that $K_{max}$ should grow with intensity, and (iii) a measurable time lag before emission. All three disagree with experiment.
The photon picture resolves this: energy arrives in quanta $h\nu$, and one photon is absorbed by one electron, giving $K_{max}=h\nu -{\varphi }_0$. This explains the existence of a threshold frequency, the independence of $K_{max}$ from intensity, and the instantaneous emission.