Planck’s interpretation in terms of quanta.

The idea

Planck proposed that the energy exchanged between matter and electromagnetic radiation is not continuous but comes in discrete packets called quanta. The energy of one quantum is directly proportional to the frequency of the radiation, E = hf, where h is the Planck constant, 6.63 × 10⁻³⁴ J s. Higher-frequency radiation therefore carries more energetic quanta, while intensity relates to the number of quanta arriving per second. This idea explained black-body radiation, where classical physics predicted an ultraviolet catastrophe.

For example: Ultraviolet light with frequency 1.0 × 10¹⁵ Hz has quanta of energy hf = 6.63 × 10⁻¹⁹ J. Planck’s quantisation was later extended by Einstein to explain the photoelectric effect, where one photon interacts with one electron.

What earns the marks

• States that energy is emitted or absorbed in discrete packets called quanta, not continuously.
• Gives the relationship E = hf, identifying h as the Planck constant with value 6.63 × 10⁻³⁴ J s.
• Explains that quantum energy is proportional to frequency, so higher frequency means more energetic quanta.
• Distinguishes intensity, which relates to the number of quanta per second, from frequency, which determines the energy of each quantum.
• Applies the idea to a context such as black-body radiation or the photoelectric effect, showing how quantisation removes the ultraviolet catastrophe or explains threshold behaviour.
• Uses correct units for energy in joules and frequency in hertz when performing calculations.

Common mistakes and how to put them right

• Treating energy as continuous and saying that any value can be emitted.

  Put it right: Energy exchange occurs in whole quanta of size hf.

• Confusing intensity with quantum energy and claiming brighter light gives more energetic quanta.

  Put it right: Intensity increases the number of quanta per second, while frequency determines each quantum’s energy.

• Using the wrong constant or unit, such as writing h as 6.63 × 10⁻³⁴ J.

  Put it right: h has units J s, and E = hf gives energy in joules.

Exam tips

• Write the equation E = hf and define every symbol before substituting values, so the examiner can see your reasoning.
• When comparing two radiations, calculate or compare hf values rather than relying on vague statements about brightness.
• Link the quantum idea explicitly to the photoelectric effect by stating that one quantum can transfer its energy to one electron.