Planck's quantum theory and the photoelectric effect

Planck's quantum theory: energy is not given out or taken in continuously, but in small packets called quanta. The energy of one quantum is E = hν, where h = 6.626 × 10⁻³⁴ J s (Planck's constant). Energy always comes in whole numbers of quanta. For light, a quantum is called a photon. For example, a photon of frequency 1.0 × 10¹⁵ Hz carries E = 6.626 × 10⁻³⁴ × 1.0 × 10¹⁵ = 6.626 × 10⁻¹⁹ J.

Black-body radiation: as a solid is heated, it first glows red, then orange and yellow, and finally white. The peak of its radiation shifts to higher frequencies as the temperature rises. Planck's quanta explained this.

The photoelectric effect: when light of the right frequency falls on a clean metal surface, electrons are ejected at once. The experiments showed:

• There is no time lag.
• The number of electrons ejected depends on the brightness (intensity) of the light.
• Their energy depends on the frequency of the light.
• Below a certain threshold frequency, ν₀, which is different for each metal, no electrons come out at all, however long or bright the light.

Einstein (1905) explained this with photons. One photon gives all its energy to one electron. Part of the energy, hν₀ (the work function, W₀), is needed to free the electron from the metal; the rest becomes its kinetic energy:

hν = hν₀ + ½mₑv², or ½mₑv² = h(ν – ν₀).

For a mole of photons, multiply the energy of one photon by Avogadro's number: E = hν × 6.022 × 10²³.