Light that knocks out electrons.

• Classical wave theory failed for black-body radiation, the photoelectric effect, the heat capacity of solids at different temperatures and the line spectra of atoms.
• A black body is an ideal absorber and emitter of all frequencies; its emission depends only on temperature. Intensity rises with wavelength to a peak and then falls, and the peak moves to shorter wavelength as temperature rises, which is why heated iron glows dull red, then brighter red, then white and then blue.
• Planck (1900): energy is emitted or absorbed only in packets called quanta, with E = hν and h = 6.626 × 10⁻³⁴ J s. Allowed energies are 0, hν, 2hν, 3hν … and nothing in between, like standing on steps of a staircase.
• Photoelectric effect (Hertz, 1887): light ejects electrons from metals such as potassium, rubidium and caesium. Ejection is instant, the number of electrons grows with brightness, and below a threshold frequency ν₀ no electron comes out at any brightness.
• Einstein (1905): light is a stream of photons; one photon gives all its energy to one electron. Energy balance: hν = hν₀ + ½mₑv², where hν₀ = W₀, the work function.
• Above the threshold, the kinetic energy of the electrons rises with frequency and does not depend on brightness; brighter light only means more photons and so more electrons.
• NCERT's work functions (eV): Li 2.42, Na 2.3, K 2.25, Mg 3.7, Cu 4.8, Ag 4.3. NCERT's text also quotes the threshold for potassium as 5.0 × 10¹⁴ Hz, so in a numerical use the value the question gives.
• Light is dual: it shows wave behaviour (interference, diffraction) while travelling and particle behaviour when it interacts with matter.

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