# Line spectra

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u26-line-spectra/

This sub-topic explains the different types of line spectra, their origin from electron transitions between discrete atomic energy levels, and their practical use for element identification in samples and astronomical sources.

**Prerequisites:** [Atomic energy levels and photon energy calculations](https://www.owlsprep.com/study/cie-9702-u26-atomic-energy-levels/)

## Learning objectives

- Distinguish between continuous, emission, and absorption line spectra
- Explain the origin of line spectra using discrete atomic energy levels
- Calculate photon wavelength/energy from energy level transitions
- Apply line spectra concepts to identify elements in unknown samples

## Types of Optical Spectra

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.

**Worked example:** 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.

## Origin of Line Spectra from Energy Transitions

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.

*Notation:* E_{\text{photon}} = |E_{\text{final}} - E_{\text{initial}}|

*Example:* An electron jumping from -1.5 eV to -13.6 eV emits a 12.1 eV photon.

$$E = hf = \frac{hc}{\lambda} = |\Delta E|$$

Each element has a unique set of energy levels, so each produces a unique line spectrum, acting as a 'spectral fingerprint' for identification.

**Worked example:** 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 eV·nm.

1. Calculate the absolute energy difference, which equals the photon energy:
2. $$|\Delta E| = |(-13.6 \text{ eV}) - (-3.40 \text{ eV})| = 10.2 \text{ eV}$$
3. Rearrange the energy-wavelength relation to solve for λ:
4. $$\lambda = \frac{hc}{E} = \frac{1240 \text{ eV·nm}}{10.2 \text{ eV}} \approx 122 \text{ nm}$$
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 10⁻⁹.

## Practical Applications of Line Spectra

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.

> **info**
>
> Helium was first discovered in 1868 via its unique absorption lines in the Sun's spectrum, 27 years before it was found on Earth.

**Worked example:** 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.

## Common pitfalls

- **Wrong:** Confusing the origin of emission and absorption spectra
  - Why it fails: Mixing up whether electrons gain or lose energy during the transition
  - Correct: Emission: electrons drop to lower energy, emit photons → bright lines on dark. Absorption: electrons jump to higher energy, absorb photons → dark lines on bright.
- **Wrong:** Forgetting to convert energy from eV to joules for SI unit calculations
  - Why it fails: Using eV energy with h in units of J·s gives an incorrect result
  - Correct: Multiply energy in eV by 1.6×10⁻¹⁹ J/eV to convert to joules before calculating wavelength in meters.
- **Wrong:** Assuming all line transitions produce visible light
  - Why it fails: Only transitions with energy differences between ~1.6 eV and ~3.3 eV produce visible photons
  - Correct: Larger energy differences produce ultraviolet photons, smaller differences produce infrared photons, both of which are invisible.
- **Wrong:** Getting a negative wavelength from negative ΔE for emission transitions
  - Why it fails: Failing to use the absolute value of the energy difference for photon energy
  - Correct: Photon energy is always positive, so take the absolute value of ΔE before calculating wavelength.

## 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 | $E_{\text{photon}} = \|\Delta E\| = \frac{hc}{\lambda}$ |

## 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.

- [Photoelectric Effect](https://www.owlsprep.com/study/cie-9702-u26-photoelectric-effect/)
- [de Broglie wavelength](https://www.owlsprep.com/study/cie-9702-u26-de-broglie-wavelength/)

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/cie-9702-u26-line-spectra/