Line spectra
CIE A-Level PhysicsΒ· Unit 26: Quantum PhysicsΒ· 15 min read
1. Types of Optical Spectraβ β ββββ± 5 min
When light is split into its component wavelengths by a prism or diffraction grating, it forms a spectrum. Spectra are classified into three main categories based on their appearance and origin.
Emission line spectrum
A pattern of discrete bright coloured lines on a dark background, produced by hot, low-density gas where excited electrons drop to lower energy levels and emit photons of specific, fixed energies.
Example:
The hydrogen emission spectrum has four distinct visible lines at red, blue-green, blue-violet, and violet wavelengths.
An absorption line spectrum is the reverse pattern: discrete dark lines on a continuous bright background. It forms when white light from a hot, dense source passes through a cool, low-density gas. The gas absorbs photons of exactly the energies matching its electron transitions, then re-emits them in random directions, leaving dark lines at those wavelengths.
A distant glowing nebula produces a spectrum with bright green lines on a completely black background. What type of spectrum is this, and what is the state of the nebula's gas?
- 1
Recall the defining feature of each spectrum type: bright lines on a dark background are characteristic of emission spectra.
- 2
Emission spectra are produced by hot, low-density excited gas. The nebula consists of low-density hydrogen and oxygen gas heated by nearby stars.
2. Origin of Line Spectra from Energy Transitionsβ β β βββ± 7 min
Line spectra are direct experimental evidence that electrons in atoms can only occupy discrete, quantized energy levels. When an electron moves between two energy levels, it emits or absorbs a photon with energy exactly equal to the difference between the two levels.
Energy level transition
A change in an electron's energy when it moves between two allowed energy levels. The energy of the emitted or absorbed photon equals the absolute value of the energy difference.
Example:
An electron jumping from -1.5 eV to -13.6 eV emits a 12.1 eV photon.
Each element has a unique set of energy levels, so each produces a unique line spectrum, acting as a 'spectral fingerprint' for identification.
An electron in a hydrogen atom transitions from n=2 (energy = -3.40 eV) to n=1 (energy = -13.6 eV). Calculate the wavelength of the emitted photon, given hc = 1240 eVΒ·nm.
- 1
Calculate the absolute energy difference, which equals the photon energy:
- 2
- 3
Rearrange the energy-wavelength relation to solve for Ξ»:
- 4
- 5
This wavelength falls in the ultraviolet region of the electromagnetic spectrum, so it is not visible to the human eye.
Exam tip:
Always check units: if your answer is supposed to be in meters, convert nanometers by multiplying by 10β»βΉ.
3. Practical Applications of Line Spectraβ β ββββ± 4 min
The unique spectral fingerprint property makes line spectra invaluable in many fields, from analytical chemistry to astronomy.
On Earth, we use emission spectra to identify trace elements in unknown samples. In astronomy, absorption spectra from starlight are used to determine which elements are present in a star's outer atmosphere, and to measure the red shift of distant galaxies to determine their speed relative to Earth.
An unknown element sample produces a line spectrum that matches exactly the published line pattern for sodium. What can we conclude about the sample?
- 1
Every element has a unique line spectrum (spectral fingerprint) because it has a unique set of atomic energy levels.
- 2
An exact match to sodium's spectrum confirms that sodium is present in the unknown sample.
4. Common Pitfalls
Wrong move:
Confusing the origin of emission and absorption spectra
Why:
Mixing up whether electrons gain or lose energy during the transition
Correct move:
Emission: electrons drop to lower energy, emit photons β bright lines on dark. Absorption: electrons jump to higher energy, absorb photons β dark lines on bright.
Wrong move:
Forgetting to convert energy from eV to joules for SI unit calculations
Why:
Using eV energy with h in units of JΒ·s gives an incorrect result
Correct move:
Multiply energy in eV by 1.6Γ10β»ΒΉβΉ J/eV to convert to joules before calculating wavelength in meters.
Wrong move:
Assuming all line transitions produce visible light
Why:
Only transitions with energy differences between ~1.6 eV and ~3.3 eV produce visible photons
Correct move:
Larger energy differences produce ultraviolet photons, smaller differences produce infrared photons, both of which are invisible.
Wrong move:
Getting a negative wavelength from negative ΞE for emission transitions
Why:
Failing to use the absolute value of the energy difference for photon energy
Correct move:
Photon energy is always positive, so take the absolute value of ΞE before calculating wavelength.
5. Quick Reference Cheatsheet
Spectrum Type | Origin | Appearance |
|---|---|---|
Continuous | Hot dense solid/liquid | All wavelengths, no lines |
Emission Line | Hot low-density excited gas | Bright lines on dark background |
Absorption Line | Cool low-density gas in front of bright source | Dark lines on continuous background |
Transition Rule | Any electron transition |
When this came up on past exams
AI-estimated based on syllabus patterns β cross-check with official past papers for accuracy. Use only as revision-focus signals.
- 2022 Β· 1
Identify spectrum type
- 2021 Β· 2
Calculate photon wavelength
- 2023 Β· 2
Explain absorption origin
Going deeper
What's Next
Line spectra provide direct experimental proof of the quantized nature of atomic energy levels, which is the core foundation of all quantum physics. Understanding this topic connects the wave-particle duality of light to atomic structure, and enables key applications in cosmology and analytical chemistry. Mastering energy transition calculations will also prepare you for more advanced quantum topics, including wave-particle duality and X-ray production.