Chemistry · Lesson

Light, atomic spectra and evidence for energy levels

Connect light wavelength and photon energy with evidence for atomic energy differences. Keep an invented level picture distinct from a measured spectrum.

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By the end, you can

Relate vacuum wavelength, frequency and photon energy.
Distinguish an atom’s energy change from the positive energy of an emitted photon.
Explain what discrete spectral lines support and what a simple atomic model leaves out.

Frequency and wavelength describe light

Light can be described as an electromagnetic wave. Frequency ν counts cycles per second and has unit hertz, Hz. Wavelength λ describes the spatial distance between corresponding wave positions. In vacuum, c = λν, where c = 299 792 458 m/s exactly in SI. A shorter vacuum wavelength corresponds to a higher frequency.

Photon energy is E = hν = hc/λ, with Planck constant h = 6.62607015 × 10⁻³⁴ J s exactly in SI. Higher frequency therefore corresponds to higher photon energy. Wavelength must be converted to the same length unit used for c. For propagation in a material, use the relevant relation rather than silently applying a vacuum wavelength formula to any measured in-material wavelength.

An atomic spectrum can contain separate lines

An excited gas of atoms can emit light at characteristic wavelengths. A suitable instrument can resolve discrete lines rather than a smooth distribution at every wavelength. Atomic absorption can also select frequencies. These observations support discrete differences between accessible atomic energy states. The spectrum is evidence; an energy-level diagram is a representation used to explain it.

For a transition between a higher and a lower state, an emitted photon has energy equal to the positive energy gap. The atom’s energy change is negative because it loses energy. For absorption, the atom gains energy. Additional selection rules affect which transitions occur, and measured line shapes can include broadening or other structure. A beginner’s level diagram should not claim that every possible pair automatically produces an equally strong line.

Read a simple gap before a real spectrum

Imagine two invented atomic levels at 0 and 3 arbitrary energy units. Their separation is 3 units. A downward transition changes the atom’s energy by −3 units while producing a photon with positive energy 3 units. An upward absorption changes the atom’s energy by +3 units. Choosing zero for the lower state here is a reference convention in a teaching model.

The table makes the signs explicit without claiming these are hydrogen data. It does not supply a wavelength because the arbitrary unit has not been related to joules. Do not combine a schematic gap labelled “3” with a real photon calculation unless the energy unit and model are defined.

One energy gap, two transition directions

Transition	Initial atomic energy	Final atomic energy	Atom ΔE	Photon energy
Absorption	0	3	+3	3, absorbed
Emission	3	0	−3	3, emitted

Invented levels at 0 and 3 arbitrary energy units. Photon energy is positive in both directions; the sign of the atom’s energy change depends on absorption or emission.

From early models toward a quantum description

The Bohr model related hydrogen’s line spectrum to allowed energies and was historically useful. A picture of electrons in circular planetary orbits is not the modern general description of atomic electrons. It also cannot be extended unchanged into an accurate general theory of many-electron atoms.

The next lessons introduce orbitals and electron configurations as quantum descriptions. Retain the energy-accounting relation supported here while changing the spatial model. Good learning connects the observation, the calculation and the limits of the model instead of treating one old drawing as a literal picture of every atom.

Worked examples

Calculate a vacuum photon energy

A hypothetical photon has vacuum wavelength 5.00 × 10² nm. Calculate its frequency and energy.

Convert wavelength: 5.00 × 10² nm = 5.00 × 10⁻⁷ m.
ν = c/λ = 299 792 458 m/s ÷ (5.00 × 10⁻⁷ m), about 6.00 × 10¹⁴ Hz.
Calculate E = hc/λ directly without rounding the intermediate frequency: about 3.9728917 × 10⁻¹⁹ J, then 3.97 × 10⁻¹⁹ J at three significant figures.

About 6.00 × 10¹⁴ Hz and 3.97 × 10⁻¹⁹ J. The assumed wavelength is not an identified measured atomic line.

Try it yourself

For two vacuum wavelengths, does the shorter one correspond to higher or lower photon energy?
Show the answer and reasoning
Higher.
E = hc/λ is inversely proportional to wavelength for fixed h and c.
An atom moves from 3 to 0 arbitrary energy units. Give its energy change and the emitted photon energy.
Show the answer and reasoning
Atom ΔE = −3 units; photon energy = +3 units.
The atom loses energy; the photon carries the positive gap.
Can an energy gap of “3 arbitrary units” alone give a wavelength in nanometres?
Show the answer and reasoning
No.
A physical energy unit or conversion is needed.
Do discrete spectral lines prove literal circular electron orbits in every atom?
Show the answer and reasoning
No.
They support energy-state differences. The spatial and many-electron description requires a more capable model.

What to carry forward

In vacuum, c = λν and E = hν.
An emitted photon carries a positive energy gap while the atom loses energy.
Label invented energy levels and their units honestly.
Spectral evidence supports energy structure without making a planetary diagram literal.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.