The big idea: An atom can only hold a few allowed energies — never the values in between. These are its energy levels (we say the energy is quantised: it comes in fixed steps).
When an electron drops from a higher level to a lower one, the energy it loses leaves as a single packet of light — a photon.
Because only certain drops are allowed, an atom gives out only certain colours — a pattern of separate lines called a line spectrum.
[Diagram: phys-energy-levels] - Available in full study mode
New words, plainly: Quantised = only fixed values are allowed (like stairs, not a ramp).
Photon = one tiny packet of light energy.
Transition = an electron jumping between two levels.
Line spectrum = the set of separate lines (colours) an atom gives out or takes in.
Emission spectrum
- Electron drops to a lower level and gives out a photon
- You see bright coloured lines on a dark background
- Each line = one allowed energy gap in the atom
Absorption spectrum
- Electron absorbs a photon and jumps up to a higher level
- You see dark lines missing from a continuous rainbow
- The same gaps are missing as the emission lines — same atom, same energies
Why a line spectrum is a fingerprint: Every element has its own set of energy levels, so it has its own pattern of lines.
That is how we match a spectrum to an element — and how we know which energy-level diagram a spectrum came from.
The energy a photon carries equals the gap between the two levels. The data booklet gives two ways to link that energy to the light:
- energy of the photon — equals the energy lost in the jump (J)
- Planck constant, 6.63 × 10⁻³⁴ J s (given)
- frequency of the emitted (or absorbed) light (Hz)
- energy of the photon — equals the energy of the jump (J)
- Planck constant, 6.63 × 10⁻³⁴ J s (given)
- speed of light, 3.00 × 10⁸ m s⁻¹ (given)
- wavelength of the light (m)
Bigger drop → shorter wavelength: From , a bigger energy gap means a bigger E, which means a shorter wavelength λ (and higher frequency).
So the biggest drop makes the shortest-wavelength line; the smallest drop makes the longest-wavelength line.
[Diagram: phys-energy-levels] - Available in full study mode
Worked example — wavelength of an emitted photon
An electron in an atom drops between two levels and loses 3.0 × 10⁻¹⁹ J of energy. Find the wavelength of the photon it emits. (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹.)
Solution
- The photon energy equals the energy lost in the jump, so start from the given wavelength formula:
- Rearrange to make the wavelength λ the subject:
- Put in the numbers (h = 6.63 × 10⁻³⁴, c = 3.00 × 10⁸, E = 3.0 × 10⁻¹⁹):
- Work it out — keep the unit:
Final answer
λ ≈ 6.6 × 10⁻⁷ m (about 660 nm — red light). A small energy gap gives a long wavelength.
Practice with real exam questions
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How this is tested: Energy levels and spectra are almost always a Paper 1A multiple-choice question.
- Paper 1A — match: match an emission-line pattern to the correct set of energy levels (more gaps → more lines). - Paper 1A — longest wavelength: pick the transition that emits the longest-wavelength photon — that is the smallest energy drop. - Paper 1A — count the lines: given an electron falling from level n to the ground state, find how many different wavelengths are possible. - Paper 2: use or to turn a level gap into a frequency or wavelength.
Classic trap: thinking the biggest drop gives the longest wavelength — it's the opposite (biggest drop = shortest λ).
Counting distinct wavelengths: Each different gap between two levels makes one line. From level n down to the ground state, the number of different downward jumps is n(n − 1) ÷ 2.
For n = 3 that is 3 lines (3→1, 3→2, 2→1); for n = 4 it is 6 lines.
[Diagram: phys-energy-levels] - Available in full study mode
IB-style question — (a) how many emission wavelengths
In a particular atom an electron is excited to the third level (n = 3). As the atoms in a sample relax, the electrons fall back to the ground state by every possible route. How many different wavelengths can appear in the emission spectrum?
Solution
- Each distinct downward jump between two levels gives one wavelength. List the jumps possible from n = 3:
- From n = 3: the jumps are 3→2, 3→1 and 2→1 — three different gaps.
- Three different energy gaps → three different photon energies → three different wavelengths.
Final answer
3 different wavelengths (3→2, 3→1 and 2→1). The shortcut n(n − 1)/2 = 3(2)/2 = 3 agrees.
IB-style question — (b) the longest-wavelength line
Using the same three levels, state which transition produces the photon with the LONGEST wavelength, and explain why.
Solution
- Longest wavelength means the smallest photon energy, because — small E ↔ large λ.
- The smallest energy drop is the jump between the two closest levels: 3→2.
- So the 3→2 jump loses the least energy and makes the longest-wavelength photon.
Final answer
The 3→2 transition (the smallest energy gap) gives the longest-wavelength photon, because a smaller energy means a larger wavelength.