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Theme E — Nuclear and Quantum Physics

E.1.3 Emission and Absorption Spectrum — IB Physics HL Revision Notes & Topical Questions

5 min read 11 parts Lesson 5 of 45 1 quiz

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Lesson summary

E.1.3 Emission and Absorption Spectrum — IB PHYSICS SL notes: Explain line spectra in terms of discrete atomic energy levels and calculate photon energies of transitions.Continuous spectrum — a hot dense solid such as an incandescent filament emits all wavelengthsEmission line sp…

  • Emission line spectrum
  • Unique pattern
  • Ground state
  • Negative energies
  • Allowed changes
  • Excitation

Part 1 of 9Types of spectrum

Types of spectrum
Continuous spectrum
  • Continuous spectrum a hot dense solid such as an incandescent filament emits all wavelengths
Emission line spectrum
  • Emission line spectrum a hot low-pressure gas, such as neon in a sign or sodium in a street lamp, emits only certain wavelengths
  • They appear as bright coloured lines on a dark background through a grating or prism.
Absorption spectrum
  • Absorption spectrum white light passed through a cool low-pressure gas has certain wavelengths missing, seen as dark lines on a continuous background
Match
  • Match the dark lines occur at exactly the same wavelengths as the bright lines of the same element
  • A hydrogen absorption spectrum is the inverse of its emission spectrum.

Part 2 of 9Spectra as fingerprints

Unique pattern
  • Unique pattern each element produces its own set of lines, and no two elements share the same set
Use
  • Use elements in laboratory samples and in stars are identified from their line patterns
Hydrogen
  • Hydrogen a strong red line at 656 nm
Sodium
  • Sodium a strong yellow line at 589 nm, giving a yellow flame
Mercury
  • Mercury most emission lines are below 450 nm, giving a blue light
Lamps
  • Lamps sodium, mercury and neon are used in street lights and coloured signs

Part 3 of 9Discrete energy levels

Energy levels
  • Energy levels line spectra show that electrons in atoms have only certain definite energies
Ground state
  • Ground state the lowest level, with higher levels called excited states
Negative energies
  • Negative energies energy is measured with the electron at infinite distance as zero, so bound levels are negative
  • Negative energy only means the electron is bound.
Hydrogen
  • Hydrogen the ground state is −13.6 eV and the levels follow En = −13.6/n2 eV
Allowed changes
  • Allowed changes an electron can change level only by gaining or losing exactly the energy difference between levels

Part 4 of 9Emission of photons

Excitation
  • Excitation heating a low-pressure gas excites electrons to higher levels
  • In a discharge tube the atoms are excited by collisions with electrons accelerated by a high voltage.
  • In a flame, thermal collisions do it.
Emission
  • Emission when an electron falls from E2 to E1, the atom emits one photon with hf = E2 − E1
  • λ = hc/(E2 − E1).
  • h = 6.63 × 10−34 J s.
Each transition
  • Each transition it gives one wavelength and so one spectral line
Large gaps
  • Large gaps they give high-frequency lines
    • (blue or ultraviolet)
Small gaps
  • Small gaps they give low-frequency lines
    • (red or infrared)

Part 5 of 9Absorption of photons

Condition
  • Condition an electron in E1 absorbs a photon only if its energy equals the gap to a higher level
Other photons
  • Other photons they pass through, so specific wavelengths are removed from the beam
Dark lines
  • Dark lines absorbed energy is re-emitted in random directions, so the intensity in the original direction is reduced

Part 6 of 9Ionisation

Ionisation energy
  • Ionisation energy the energy needed to remove an electron from the ground state completely, 13.6 eV for hydrogen
Excess energy
  • Excess energy a photon or collision with more energy than this ionises the atom, and the excess becomes kinetic energy of the freed electron
Spectrum
  • Spectrum the ionising spectrum is continuous because the ejected electron may have any kinetic energy

Part 7 of 9Spectra of stars

Sun's spectrum
  • Sun's spectrum its surface gives a continuous spectrum crossed by dark Fraunhofer lines from gases in the cooler outer atmosphere
Identification
  • Identification comparing line positions with laboratory spectra identifies the elements present
  • Helium was first discovered in the Sun this way.
Red shift
  • Red shift lines shifted to longer wavelengths show a star moving away from us
Wavelength measurement
  • Wavelength measurement a diffraction grating, d sin θ = nλ, measures wavelengths and so energy-level differences
    What the symbols mean: d = grating spacing (m) · θ = angle of the nth-order maximum · n = order number (0, 1, 2 …) · λ = wavelength (m)

Part 8 of 9Energy level diagrams

Layout
  • Layout levels are horizontal lines at heights proportional to energy, with vertical arrows for transitions
  • Longer arrows mean higher-frequency photons.
Number of lines
  • N levels allow N(N − 1)/2 lines if all transitions are allowed, so four levels give six lines
Method
  • Method find the differences between pairs of levels and convert each to a wavelength with λ = hc/ΔE
  • hc = 1.99 × 10−25 J m or 1240 eV nm.
Units
  • Units convert eV to joules (1 eV = 1.60 × 10−19 J) before using hf = E with SI values

Part 9 of 9More from the specification

Rutherford Alpha Particle Scattering Experiment
  • Bombarding thin gold foil with energetic alpha particles revealed that most particles pass straight through without deflection,
  • while a small fraction deflect through angles greater than 90°.
Discovery of the Atomic Nucleus
  • Rutherford's scattering observations demonstrated that the atom consists mostly of empty space, with virtually all positive charge and mass concentrated in a tiny central nucleus.
Atomic Emission Spectra and Energy Levels
  • When excited atomic electrons transition between quantised energy levels, photons of discrete frequencies are emitted according to the Planck-Einstein equation ΔE = h f = h c / λ.
Atomic Absorption Spectra
  • Passing continuous white light through a cool gas produces dark absorption lines at specific wavelengths, matching the photon energies absorbed by electrons transitioning to higher energy states.
Rutherford Alpha Particle Scattering Experiment
  • Bombarding thin gold foil with energetic alpha particles revealed that most particles pass straight through without deflection,
  • while a small fraction deflect through angles greater than 90°.
Discovery of the Atomic Nucleus
  • Rutherford's scattering observations demonstrated that the atom consists mostly of empty space, with virtually all positive charge and mass concentrated in a tiny central nucleus.
Atomic Emission Spectra and Energy Levels
  • When excited atomic electrons transition between quantised energy levels, photons of discrete frequencies are emitted according to the Planck-Einstein equation ΔE = h f = h c / λ.
Atomic Absorption Spectra
  • Passing continuous white light through a cool gas produces dark absorption lines at specific wavelengths, matching the photon energies absorbed by electrons transitioning to higher energy states.
Nucleus
  • Small, dense, positively charged centre of the atom.
Scattering
  • Deflection of particles from their original path.
Alpha particle
  • Helium nucleus, charge +2.
Nuclear notation
  • Symbol showing mass number and atomic number.
Rutherford scattering
  • Scattering of charged particles by a nucleus through electrostatic repulsion alone.
Subatomic particle
  • A particle smaller than an atom, e.g. the electron.

Key terms

TermMeaning
Line spectrumSpectrum with only certain wavelengths, characteristic of the element.
Energy levelAllowed energy of a bound electron in an atom.
Ground stateLowest energy level of an atom.
Ionisation energyEnergy needed to remove an electron from the ground state.
Absorption spectrumDark lines on a continuous background from gas absorbing photons.
PhotonA quantum of electromagnetic radiation with energy hf.

Avoid these mistakes

1
Thinking a photon of any energy can be absorbed — only photons matching an energy gap, or exceeding the ionisation energy, are absorbed.
2
Confusing the spectra — emission lines are bright on a dark background and absorption lines are dark on a continuous spectrum.
3
Taking negative energies to mean the electron has less than zero energy in a physical sense — it only means the electron is bound.
4
Forgetting to convert eV to joules before using hf = E with SI values.
5
Believing the spectrum of a hot dense solid is a line spectrum — it is continuous.

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