IB Physics SL

Revision Notes

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:

2.5.2 Wavelength 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)

Calculating-Discrete-Energies-Worked-Example---Calculating-Discrete-Energies-Answer, downloadable AS & A Level Physics revision notes

  • 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)

2.5.2 Energy Levels Worked Example


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