Atomic transitions and light

Why does an atom emit particular colors?

Connect a modeled hydrogen transition to photon energy and wavelength while separating position from intensity.

An atom can occupy particular energy states. When it emits a photon during a transition to a lower state, the photon carries the energy difference. Select a hydrogen transition to connect the energy diagram with a spectral position. The diagram shows energy states, not an electron’s planetary path.

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EXPLORE THE MODEL

Connect an energy change to light

Reduced-mass Rydberg teaching calculation in vacuum; not evaluated NIST lines. Fine structure and higher corrections are omitted.

Initial energy level n3

TEACHING RELATIONSHIPΔE = hc / λ

Transitionn = 3 → 2

Vacuum wavelength656.5 nm

Photon energy1.889 eV

A larger energy drop produces a higher-energy photon with a shorter wavelength.

Compare the separate NIST handbook reference records

These selected H I records use air wavelengths. The plot above uses approximate vacuum Rydberg calculations. They are deliberately not overlaid as interchangeable values.

Transition family	Air wavelength (nm)	Source reference
n=6 → 2	410.174	RCWM80
n=5 → 2	434.0462	MK00a
n=4 → 2	486.12786	MK00a
n=4 → 2	486.1287	MK00a
n=4 → 2	486.13615	MK00a
n=3 → 2	656.2711	MK00a
n=3 → 2	656.27248	MK00a
n=3 → 2	656.28518	MK00a

The table includes selected fine-structure components. MK00a is a calculation reference; the records are not uniformly measured laboratory lines. Unknown uncertainties remain unspecified.

Inspect the original NIST table ↗

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HOW DO WE KNOW?

Evidence & limits

Reference science + bounded teaching model

What this interaction establishes

Connect a modeled hydrogen transition to photon energy and wavelength while separating position from intensity.

Reduced-mass Rydberg teaching calculation in vacuum; not evaluated NIST lines. Fine structure and higher corrections are omitted.

Source bindings for this explanation

Start here

Sources: S05, S06, SRC-CODATA.

Explore the science

Photon energy satisfies ΔE = hν = hc/λ in vacuum. The interactive readout uses a reduced-mass Rydberg approximation for transitions ending at n = 2; a larger energy drop gives a shorter wavelength. These calculated vacuum positions are not evaluated NIST lines. A separate NIST handbook table lists reference wavelengths in air. Line position alone does not determine brightness, which also depends on populations, transition probabilities, source conditions and detection.

Sources: S05, S06, SRC-CODATA.

Go deeper

The teaching calculation omits fine structure, QED and further recoil corrections. A rounded model position therefore need not equal a resolved reference component. The handbook's visible hydrogen entries use air wavelengths, whereas the model uses vacuum wavelengths: λair = λvacuum/n for the relevant refractive index. Keep the table's units and convention visible. Raw differences between these two displays mix model approximation with wavelength convention; they are not directly a measurement error or a physical redshift.

Sources: S05, S06, SRC-CODATA.

Limitations

The diagram uses calculated reduced-mass Rydberg energies and does not depict an electron trajectory. The model gives approximate vacuum wavelengths; the separate NIST handbook reference table uses air wavelengths for these visible lines. Fine structure and higher corrections are omitted; wavelength alone does not establish brightness or abundance.

Sources: S05, S06, SRC-CODATA.

Keep these boundaries in mind

The diagram uses calculated reduced-mass Rydberg energies and does not depict an electron trajectory.
The model gives approximate vacuum wavelengths; the separate NIST handbook reference table uses air wavelengths for these visible lines.
Fine structure and higher corrections are omitted; wavelength alone does not establish brightness or abundance.

Inspect the references

Supplemental primary reference ↗Supplemental primary reference ↗Supplemental primary reference ↗

Scientific explanations with linked references. Model calculations retain their stated assumptions and limits.

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MAKE THE CONNECTION YOUR OWN

Test your reasoning

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recognition

In an emission event, what does the photon carry away?

The atom’s full massEnergy corresponding to a difference between statesA proton that changes hydrogen into helium

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mechanism

For photons in vacuum, which transition energy gives a shorter wavelength?

A smaller energy differenceAll energy differences produce one wavelengthA larger energy difference

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evidence

A line is at a reference hydrogen wavelength. Which additional claim is unsupported by that position alone?

The exact amount of hydrogen in the sourceThat the position can be compared with a referenceThat wavelength can be stated with units

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transfer

A ultraviolet photon has a shorter vacuum wavelength than a red photon. Which has more energy?

The red photon because its color is warmerThe ultraviolet photonThey must have equal energy because both are light

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Identity and isotopes Next: Operate a laboratory spectrometer