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 = E2 – E1
- 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
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.
- 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)