Discrete Energy Levels (DP IB Physics: SL)

The Photon Model

• Photons are fundamental particles that make up all forms of electromagnetic radiation
• A photon is a massless “packet” or a “quantum” of electromagnetic energy
• What this means is that the energy is not transferred continuously but as discrete packets of energy
• In other words, each photon carries a specific amount of energy, and transfers this energy all in one go

Calculating Photon Energy

• The energy of a photon can be calculated using the formula:

E = hf

• Using the wave equation, energy can also be equal to:

• Where:
  • E = energy of the photon (J)
  • h = Planck's constant (J s)
  • c = the speed of light (m s^-1)
  • f = frequency (Hz)
  • λ = wavelength (m)

• This equation tells us:
  • The higher the frequency of EM radiation, the higher the energy of the photon
  • The energy of a photon is inversely proportional to the wavelength
  • A long-wavelength photon of light has a lower energy than a shorter-wavelength photon

Atomic Energy Levels

• Electrons in an atom can have only certain specific energies
  • These energies are called electron energy levels

• They can be represented as a series of stacked horizontal lines increasing in energy
• Normally, electrons occupy the lowest energy level available, this is known as the ground state
• Electrons can gain energy and move up the energy levels if it absorbs energy either by:
  • Collisions with other atoms or electrons
  • Absorbing a photon
  • A physical source, such as heat

• This is known as excitation, and when electrons move up an energy level, they are said to be in an excited state
• If the electron gains enough energy to be removed from the atom entirely, this is known as ionisation
• When an electron returns to a lower energy state from a higher excited state, it releases energy in the form of a photon

Electron energy levels in atomic hydrogen. Photons are emitted when an electron moves from a higher energy state to a lower energy state

Step 1: Outline the meaning of atomic spectra

• • Atomic spectra show the spectrum of discrete wavelengths emitted or absorbed by a specific atom

Step 2: Describe the relationship between energy and wavelength

• • Photon energy is related to frequency and wavelength by
  • Therefore, photons with discrete wavelengths have discrete energies equal to the difference between two energy levels or 

Step 3: Explain how atomic spectra give evidence for the quantisation of energy 

• • Photons arise from electron transitions between energy levels
  • This happens when an electron is excited or de-excited from one energy level to another, by either emitting or absorbing light of a specific wavelength
  • Since atomic spectra are made up of discrete wavelengths, this shows that atoms must contain discrete, or quantised, energy levels