Classical physics treats energy and matter as continuous, deterministic, and locally well behaved. For many everyday systems this works extremely well, but it breaks down when we look at atomic-scale phenomena, thermal radiation at short wavelengths, or the behavior of light and matter in carefully controlled experiments.

A blackbody is an idealized object that absorbs and emits radiation perfectly. Classical theory predicted the ultraviolet catastrophe: an unphysical divergence of emitted energy at high frequency. Planck resolved this by proposing quantized emission, with energies $$E = nh\nu$$ for integers $n$.

Light can eject electrons from a metal only if its frequency exceeds a threshold. Increasing intensity alone cannot overcome this threshold. Einstein explained this by treating light as photons with energy $E = h\nu$.

Atoms emit and absorb only specific wavelengths, producing discrete spectral lines. Classical orbiting-charge models could not explain this stability or the sharpness of the lines.