7.1.2 Calculating Discrete Energies

Transitions Between Energy Levels

Difference in discrete energy levels

• The difference between two energy levels is equal to a specific photon energy
• The energy (hf) of the photon is given by:

ΔE = hf = E2E1

• Where:
• E1 = Energy of the higher level (J)
• E2 = Energy of the lower level (J)
• h = Planck’s constant (J s)
• f = Frequency of photon (Hz)
• Using the wave equation, the wavelength of the emitted, or absorbed, radiation can be related to the energy difference by the equation: • This equation shows that the larger the difference in energy of two levels ΔE (E2 – E1) the shorter the wavelength λ and vice versa

Worked Example

Some electron energy levels in atomic hydrogen are shown below. The longest wavelength produced as a result of electron transitions between two of the energy levels is 4.0 × 10–6 m.

a) Draw and mark:

• The transition giving rise to the wavelength of 4.0 × 10–6 m with letter L.
• The transition giving rise to the shortest wavelength with letter S.

b) Calculate the wavelength for the transition giving rise to the shortest wavelength.

Part (a) • Photon energy and wavelength are inversely proportional
• Therefore, the largest energy change corresponds to the shortest wavelength (line S)
• The smallest energy change corresponds to the longest wavelength (line L)

Part (b) Close Close