Quantum theory by Planck explains that there are other factors influencing the energy emitted apart from frequency.
Continuous energy versus discrete energy:
1. The continuous spectrum of visible light is an example of continuous energy.
2. The wavelength of visible light can be of any value between \(400 nm\) and \(750 nm\).
3. There is no separation gap between each colour in the visible light spectrum.
4. The emission line spectrum from a hot mercury vapour lamp is an example of discrete energy.
5. Lights emitted are of certain fixed wavelengths and frequencies, resulting in lights (lines) of different colours.
6. Since the line spectrum produced by each element has a series of its own distinctive lines, the line spectrum can be used to identify the presence of an element.
Quantum of energy is discrete energy packet and not a continuous energy:
1. Planck explained that energy is quantised, that is, in discrete packets.
2. Einstein stated that photon is the quantum (discrete energy packet) of light.
3. Energy of a photon,\[
  E=h f
  \]
  where
  \(h=\) Planck’s constant \(
  \left(6.63 \times 10^{-34} J s \right)
  \)
  \(f=\) frequency of light wave
  Hence, \(E \propto f\), that is, energy of a photon is directly proportional to its frequency.
4. The energy depends on the frequency of the wave. The higher the frequency of a light wave, the higher the energy quantum of a photon.

Example

Radio waves from a certain station have a wavelength of \(25 m\). Determine the energy of a photon of the radio waves.

Solution
\[
\begin{aligned}
E & =h f \\
& =\frac{h c}{\lambda} \\
& =\frac{\left(6.63 \times 10^{-34}\right)\left(3 \times 10^8\right)}{25} \\
& =7.96 \times 10^{-27} J
\end{aligned}
\]

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