Energy Levels & Photon Emission (AQA A Level Physics)

• Energy levels can be represented as a series of horizontal lines
  • The line at the bottom with the greatest negative energy represents the ground state
  • The lines above the ground state with decreasing energies represent excited states
  • The line at the top, usually 0 V or infinity , represents the ionisation energy

Energy Levels in a Hydrogen Atom

A photon is emitted when an electron moves from a higher energy state to a lower energy state. The energy of the emitted photon is equal to the difference in energy between the energy levels in the transition.

Line Spectra

• Line spectra occur when excited atoms emit light of certain wavelengths which correspond to different colours
• The emitted light can be observed as a series of lines with spaces in between
  • These series of lines are called line or atomic spectra

• Each element produces a unique set of spectral lines
• No two elements emit the same set of spectral lines, therefore, elements can be identified by their line spectrum
• There are two types of line spectra: emission spectra and absorption spectra

Emission Spectra

• When an electron transitions from a higher energy level to a lower energy level, this results in the emission of a photon
• Each transition corresponds to a different wavelength of light and this corresponds to a line in the spectrum
• The resulting emission spectrum contains a set of discrete wavelengths, represented by coloured lines on a black background
• Each emitted photon has a wavelength which is associated with a discrete change in energy, according to the equation:

• Where:
  • ΔE = change in energy level (J)
  • h = Planck’s constant (J s)
  • f = frequency of photon (Hz)
  • c = the speed of light (m s^-1)
  • λ = wavelength of the photon (m)

• Line spectra provide evidence that electrons in atoms can only transition between discrete energy levels

Emission spectrum of Hydrogen gas

Absorption Spectra

• An atom can be raised to an excited state by the absorption of a photon
• When white light passes through a cool, low pressure gas it is found that light of certain wavelengths are missing
  • This type of spectrum is called an absorption spectrum

• An absorption spectrum consists of a continuous spectrum containing all the colours with dark lines at certain wavelengths
• These dark lines correspond exactly to the differences in energy levels in an atom
• When these electrons return to lower levels, the photons are emitted in all directions, rather than in the original direction of the white light
  • Therefore, some wavelengths appear to be missing

• The wavelengths missing from an absorption spectrum are the same as their corresponding emission spectra of the same element

Absorption spectrum of Hydrogen gas

• 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

• 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 

• This equation shows that the larger the difference in energy between two levels ΔE (E₂ - E₁) the shorter the wavelength λ and vice versa

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)