Atomic Energy Levels and Transitions | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Electrons in isolated atoms have discrete energies

An isolated atom is considered on its own, without neighbouring atoms changing its electron energies.

An electron in an isolated atom can occupy only particular energy levels. It cannot have an energy between two allowed levels.

Definition

1 mark

What is meant by the ground state?

Model answer: The ground state is the lowest energy state of an atom.

Any allowed state above the ground state is an excited state. An atom is excited when one of its electrons has moved to a higher allowed energy level.

Some energy-level diagrams define 0 eV as a free electron at rest far from the atom. Bound states then have negative energies. A level at −2 eV is higher than a level at −5 eV because it is closer to zero.

Reaching 0 eV removes the electron from the atom. This is ionisation, not another bound energy level.

A transition transfers one energy gap

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Energy increases upwards. A transition uses one photon. Downward transition: emission. Upward transition: absorption, but only when the photon energy exactly equals the gap.

A downward transition releases one photon. An upward transition can occur when the atom absorbs a photon whose energy exactly matches the gap. A collision can also transfer energy and excite the atom.

hf=E_{\mathrm{high}}-E_{\mathrm{low}}

Symbols

$h$ = Planck constant (J s)
$f$ = frequency of the photon (Hz)
$E_{\mathrm{high}}$ = higher electron energy level (J or eV)
$E_{\mathrm{low}}$ = lower electron energy level (J or eV)

Key idea

Use one energy unit throughout a calculation. With Planck's constant in J s, convert energy levels from eV to J before using the photon-frequency relation.

A larger energy gap produces a higher-frequency photon and a shorter wavelength. A smaller gap produces a longer wavelength.

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Transition	Energy transfer	Spectrum
Electron moves down	one photon is emitted with energy equal to the gap	emission line
Electron moves up after absorbing light	one photon with exactly the gap energy is absorbed	absorption line

Common mistake

The longest-wavelength photon comes from the smallest energy gap, not the largest vertical jump.

Your turntransition check

Two downward transitions have energy gaps of 2.0 eV and 4.0 eV. Which transition emits the shorter-wavelength photon?

Show worked answer

The 4.0 eV transition. A larger energy gap gives a higher photon frequency and therefore a shorter wavelength.