Energy Levels & Photon Emission (AQA AS Physics): Revision Note

Line spectra & energy levels

• 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 $\infty$, represents the ionisation energy

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:

$∆E=hf=\frac{hc}{\lambda }$

• Where:

  • $∆E$ = change in energy level (J)

  • $h$ = Planck’s constant (J s)

  • $f$ = frequency of photon (Hz)

  • $c$ = the speed of light (m s^-1)

  • $\lambda$ = wavelength of the photon (m)

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

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

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:

$∆E=hf=E_2-E_1$

• Where:

  • $E_1$ = Energy of the higher level (J)

  • $E_2$ = 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 

$\lambda =\frac{hc}{E_2-E_1}$

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