3.2.2.2–3Quantum PhenomenaStretch

Electron Collisions and Energy Levels

An electron bound to an atom can’t have just any energy — it can only occupy one of a fixed ladder of $discrete energy levels$ . Push it up a rung with a well-aimed collision or a perfectly-matched photon, and it will eventually fall back down, releasing the energy difference as light of one exact colour. Do this for every atom in a hot gas and you get a $line spectrum$ — a barcode that reveals an atom’s internal structure from millions of kilometres away.

40 min Video by Science Shorts 3.2.2 Electromagnetic radiation and quantum phenomena

Energy Levels & Emission Spectra — A-level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Describe atomic energy levels as discrete and (by convention) negative, with zero corresponding to an ionised, free electron
Distinguish excitation and ionisation caused by electron collision from excitation caused by photon absorption
Calculate the photon energy, frequency and wavelength emitted in a transition between two energy levels
Explain the ionisation energy of an atom
Explain how discrete energy levels produce line emission and line absorption spectra

Discrete energy levels

An electron bound within an atom can only exist in one of a set of fixed $energy levels$ , unique to that type of atom. These levels are conventionally given negative energies, because energy must be $supplied$ to remove ("free") the electron entirely — the free, unbound electron is defined as having zero energy, so every bound state sits below it. The lowest (most negative) level is the $ground state$ , where an electron sits if left undisturbed.

When an electron absorbs enough energy to move from the ground state to a higher (less negative) level, it is $excited$ . If it absorbs enough energy to reach (or exceed) zero energy, it escapes the atom completely — this is $ionisation$ , and the minimum energy required from the ground state is the atom’s $ionisation energy$ .

Tip — Always sketch energy levels as horizontal lines with negative values, ground state at the bottom, and 0 (unbound) at the top — it makes every calculation about transitions much harder to get backwards.

Two ways to excite an atom

Excitation can happen by $electron collision$ : a free electron (for example, accelerated across a discharge tube) collides with an atom and transfers some of its kinetic energy to one of the atom’s bound electrons. Because the free electron can have any amount of kinetic energy, and only needs to transfer $at least$ the energy of a particular gap (keeping any leftover energy as its own remaining kinetic energy), collision excitation is not limited to exact energy matches.

Excitation can also happen by $photon absorption$ : here the electron can absorb a photon only if the photon’s energy $h f$ matches $exactly$ the gap between its current level and a higher one. A photon is either absorbed completely or not at all — there’s no such thing as a partially-absorbed photon leaving a "leftover" — so if $h f$ doesn’t exactly equal an available energy gap, that photon simply passes straight through unaffected.

Tip — Collision: energy just needs to be enough (excess stays as kinetic energy of the colliding electron). Absorption: energy must match a gap exactly, with nothing spare.

Photon emission and transition energies

An excited electron does not stay in a higher level indefinitely — it falls back down, either directly to the ground state or via intermediate levels, and each downward transition releases a photon whose energy exactly equals the difference between the two levels involved.

Because the possible energy levels are fixed for a given type of atom, only a limited, discrete set of transition energies — and hence only a discrete set of photon frequencies and wavelengths — are possible. This is the physical origin of atomic line spectra.

h f = E_{1} - E_{2}

Photon energy released falling from a higher level E₁ to a lower level E₂ (both negative, E₁ > E₂).

1Energy released:

Δ E = (- 1.51) - (- 3.40) = 1.89

eV.

2Convert to joules:

Δ E = 1.89 \times 1.60 \times 1 0^{- 19} = 3.02 \times 1 0^{- 19}

3Use

h f = Δ E \Rightarrow f = \frac{3.02 \times 1 0 ^{- 19}}{6.63 \times 1 0 ^{- 34}} = 4.56 \times 1 0^{14}

Hz.

Answer

f \approx 4.56 \times 1 0^{14}

Hz (visible light, in this case a red hydrogen line).

Tip — Always subtract the more negative (lower) level from the less negative (higher) level to get a positive energy released — a negative answer means you have the transition direction backwards.

Line spectra

Pass the light from a hot, low-pressure gas through a spectrometer and you see a $line emission spectrum$ : a series of bright, coloured lines on an otherwise dark background, each line corresponding to one specific downward transition and hence one specific photon energy.

Pass white light (a continuous spectrum) through a cooler gas of the same element and you instead see a $line absorption spectrum$ : a continuous rainbow with thin dark lines at exactly the same wavelengths as the emission lines, where atoms have absorbed photons of just the right energy to jump between their own energy levels. Because every element has a unique set of energy levels, its line spectrum is a unique fingerprint — this is how astronomers identify the elements present in distant stars.

Tip — Line spectra are the single strongest piece of evidence that atomic energy levels are discrete rather than continuous — a continuous range of energies would give a continuous spectrum, not sharp lines.

Equation recap

h f = E_{1} - E_{2}

Photon energy from an energy-level transition.

1 eV = 1.60 \times 1 0^{- 19} J

Electronvolt to joule conversion.

Common mistakes to avoid

Thinking a photon can be partially absorbed if its energy doesn’t exactly match an energy gap.

Photon absorption is all-or-nothing — if hf doesn’t exactly equal an available transition energy, the photon is not absorbed at all.

Treating electron-collision excitation the same as photon absorption.

A colliding electron only needs to supply at least the energy of the gap, keeping any excess as its own kinetic energy — unlike a photon, which must match the gap exactly.

Forgetting energy levels are negative and subtracting them the wrong way round.

Photon energy released = (higher, less negative level) − (lower, more negative level); this always gives a positive result.

Key takeaways

Bound electrons occupy discrete, negative energy levels; 0 eV represents a free (unbound) electron.
Collision excitation only needs enough energy (excess stays as kinetic energy); photon absorption needs an exact energy match.
A photon is emitted when an electron falls between levels, with energy hf = E₁ − E₂.
Ionisation energy is the energy needed to remove a ground-state electron completely (raise it to 0 eV).
Discrete energy levels produce line emission and line absorption spectra — a unique fingerprint for each element.

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Electron Collisions and Energy Levels

An electron bound to an atom can’t have just any energy — it can only occupy one of a fixed ladder of

discrete energy levels

. Push it up a rung with a well-aimed collision or a perfectly-matched photon, and it will eventually fall back down, releasing the energy difference as light of one exact colour. Do this for every atom in a hot gas and you get a

line spectrum

— a barcode that reveals an atom’s internal structure from millions of kilometres away.

40 min Video by Science Shorts 3.2.2 Electromagnetic radiation and quantum phenomena