WJEC Eduqas Eduqas 2020-style practice: An atom emits a photon as an electron falls from an energy level of -3.0 × 10^-19\ J to a level of -8.4 × 10^-19\ J. Calculate the frequency and wavelength of the emitted photon. Take h = 6.63 × 10^-34\ J s and c = 3.0 × 10^8\ m s^-1.

The photon energy equals the difference between the levels: E = E_2 - E_1 = (-3.0 × 10^-19) - (-8.4 × 10^-19) = 5.4 × 10^-19\ J. Frequency from E = hf: f = Eh = 5.4 × 10^-196.63 × 10^-34 = 8.14 × 10^14\ Hz. Wavelength from c = fλ: λ = cf = 3.0 × 10^88.14 × 10^14 = 3.7 × 10^-7\ m, about 370\ nm. Markers reward the photon energy from the level difference, the frequency about 8.1 × 10^14\ Hz, and the wavelength about 370\ nm.

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How does a laser produce an intense, coherent beam through stimulated emission and population inversion?

Lasers: discrete energy levels and photon emission, spontaneous and stimulated emission, population inversion and the metastable state, and the properties of laser light.

A focused answer to the Eduqas A-Level Physics Component 3 lasers content, covering discrete atomic energy levels and photon emission, the difference between spontaneous and stimulated emission, population inversion and the role of a metastable state, and the properties of laser light.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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Quick answer

Atoms have discrete (quantised) energy levels; an electron falling from a higher level $E_2$ to a lower level $E_1$ emits a photon of energy $hf = E_2 - E_1$ . In spontaneous emission an excited atom drops at random, emitting a photon in any direction. In stimulated emission a passing photon of the right energy triggers an excited atom to drop, emitting a second photon identical in frequency, phase, direction and polarisation, so the light is amplified. Laser action requires a population inversion (more atoms in the excited state than the lower state) so that stimulated emission dominates absorption, made possible by a metastable state with a long lifetime where atoms accumulate. Laser light is monochromatic, coherent, collimated (a narrow beam) and intense.

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What this dot point is asking

Eduqas wants you to explain that atoms have discrete energy levels and emit photons when electrons fall between them, distinguish spontaneous from stimulated emission, define population inversion and explain the role of a metastable state, and state the properties of laser light.

The answer

Discrete energy levels and photon emission

Spontaneous and stimulated emission

Population inversion and the metastable state

Properties of laser light

Energy level gap from a laser wavelength

A helium-neon laser emits red light of wavelength $633\ \text{nm}$ . Find the energy gap between the two levels involved. Take $h = 6.63 \times 10^{-34}\ \text{J s}$ and $c = 3.0 \times 10^{8}\ \text{m s}^{-1}$ .

step 1: Use the photon energy from the wavelength

$E = \dfrac{hc}{\lambda} = \dfrac{(6.63 \times 10^{-34})(3.0 \times 10^{8})}{633 \times 10^{-9}}$ .

step 2: Evaluate the numerator and divide

$E = \dfrac{1.989 \times 10^{-25}}{6.33 \times 10^{-7}} = 3.14 \times 10^{-19}\ \text{J}$ .

step 3: Convert to electronvolts (optional)

$E = \dfrac{3.14 \times 10^{-19}}{1.6 \times 10^{-19}} = 2.0\ \text{eV}$ , the gap between the laser's upper and lower levels.

Examples in context

Lasers are everywhere: barcode and QR scanners, CD, DVD and Blu-ray players, fibre-optic communication, laser printing, surveying and spirit levels, laser cutting and welding in industry, and laser eye surgery and other medical procedures. Their coherence makes them essential to interferometry, including the detection of gravitational waves, and their monochromaticity underpins precision spectroscopy and atomic clocks.

Try this

Q1. State the equation linking the photon energy to two atomic energy levels. [1 mark]

Cue. $hf = E_2 - E_1$ , the difference between the levels.

Q2. State two properties of laser light that distinguish it from the light of a filament lamp. [2 marks]

Cue. It is monochromatic and coherent (also collimated and intense).

Q3. State what is meant by population inversion. [2 marks]

Cue. A condition in which more atoms are in the excited state than in the lower state, so stimulated emission dominates absorption.

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20204 marksAn atom emits a photon as an electron falls from an energy level of

-3.0 \times 10^{-19}\ \text{J}

to a level of

-8.4 \times 10^{-19}\ \text{J}

. Calculate the frequency and wavelength of the emitted photon. Take

h = 6.63 \times 10^{-34}\ \text{J s}

and

c = 3.0 \times 10^{8}\ \text{m s}^{-1}

Show worked answer →

The photon energy equals the difference between the levels: $E = E_2 - E_1 = (-3.0 \times 10^{-19}) - (-8.4 \times 10^{-19}) = 5.4 \times 10^{-19}\ \text{J}$ .

Frequency from $E = hf$ : $f = \dfrac{E}{h} = \dfrac{5.4 \times 10^{-19}}{6.63 \times 10^{-34}} = 8.14 \times 10^{14}\ \text{Hz}$ .

Wavelength from $c = f\lambda$ : $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^{8}}{8.14 \times 10^{14}} = 3.7 \times 10^{-7}\ \text{m}$ , about $370\ \text{nm}$ .

Markers reward the photon energy from the level difference, the frequency about $8.1 \times 10^{14}\ \text{Hz}$ , and the wavelength about $370\ \text{nm}$ .

Eduqas 20224 marksExplain what is meant by stimulated emission and population inversion, and state why a metastable state is needed for laser action.

Show worked answer →

Stimulated emission occurs when a passing photon, whose energy matches the gap between an excited level and a lower level, causes an excited atom to drop and emit a second photon identical in frequency, phase, direction and polarisation to the first.

Population inversion is the condition in which more atoms are in the excited (upper) state than in the lower state, the reverse of the normal thermal situation. It is required so that stimulated emission outweighs absorption, allowing the photon number to grow.

A metastable state is an excited level with an unusually long lifetime. Atoms accumulate there (rather than decaying at once by spontaneous emission), which makes it possible to build and maintain the population inversion. Markers reward the definition of stimulated emission (identical photon), the definition of population inversion, and the role of the metastable state in sustaining the inversion.

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Sources & how we know this

Eduqas GCE AS/A Level Physics specification (A720QS) — WJEC Eduqas (2015)