State the equation linking the frequency of an emitted photon to a change of energy level, defining each symbol.

hf = ΔE, where h is the Planck constant in J s, f is the frequency of the emitted or absorbed photon in Hz and ΔE is the difference in energy between the two levels in joules.

What is an emission line spectrum?

An emission line spectrum is a set of separate bright coloured lines on a dark background, each line corresponding to a photon emitted as an electron falls between two particular energy levels.

What is an absorption line spectrum?

An absorption line spectrum is a continuous spectrum crossed by dark lines, formed when a cool gas absorbs from a continuous source exactly those photon energies that match its own energy level differences.

Why is the line spectrum of an element unique to that element?

Every element has its own particular set of energy levels, so the set of possible differences between them, and therefore the set of photon energies emitted or absorbed, is different for each element.

CCEA A-Level Physics 1210

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Quantum Physics

Line spectra and the equation hf = ΔE

3 things to know
Unit AS 2

Overview

Emission line spectrum and absorption line spectrum.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Write the energy level transition equation in terms of the wavelength of the photon.

Numbers

An electron in hydrogen falls from the −3.4 eV level to the −13.6 eV level. Calculate the wavelength of the photon emitted.

Numbers

An electron falls between two levels separated by 1.9 eV. Calculate the wavelength of the emitted photon and name the region of the spectrum.

Questions from this subtopic

Each one with the model answer underneath.

1
State the equation linking the frequency of an emitted photon to a change of energy level, defining each symbol.
Model answer
hf = ΔE, where h is the Planck constant in J s, f is the frequency of the emitted or absorbed photon in Hz and ΔE is the difference in energy between the two levels in joules.
2
Write the energy level transition equation in terms of the wavelength of the photon.
Model answer
hc/λ = ΔE, where h is the Planck constant, c is the speed of light in a vacuum, λ is the wavelength of the photon in metres and ΔE is the energy difference in joules.
3
What is an emission line spectrum?
Model answer
An emission line spectrum is a set of separate bright coloured lines on a dark background, each line corresponding to a photon emitted as an electron falls between two particular energy levels.
4
What is an absorption line spectrum?
Model answer
An absorption line spectrum is a continuous spectrum crossed by dark lines, formed when a cool gas absorbs from a continuous source exactly those photon energies that match its own energy level differences.
5
Why is the line spectrum of an element unique to that element?
Model answer
Every element has its own particular set of energy levels, so the set of possible differences between them, and therefore the set of photon energies emitted or absorbed, is different for each element.
6
An electron in hydrogen falls from the −3.4 eV level to the −13.6 eV level. Calculate the wavelength of the photon emitted.
Model answer
ΔE = 10.2 eV = 10.2 × 1.60 × 10⁻¹⁹ = 1.63 × 10⁻¹⁸ J, so λ = hc/ΔE = 1.989 × 10⁻²⁵ / 1.63 × 10⁻¹⁸ = 1.22 × 10⁻⁷ m, that is 122 nm, and hc ÷ 1.22 × 10⁻⁷ m returns 1.63 × 10⁻¹⁸ J.

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