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Course homeModule I-13 · Recommended before: Before light and electronic structure
Photon energy, wavelength and frequency
Wavelength, frequency and energy connect atomic transitions to observable light. These equations require exponent handling and consistent SI units.
Learn the method
c = λν; E = hν = hc/λ
- Convert nanometers to meters.
- Compute frequency as c/λ.
- Compute photon energy as hν = hc/λ.
- Report energy per photon in joules.
- Check whether shorter wavelength gives greater energy.
Common mistake: A photon wavelength of 500 nm is 5.00 × 10⁻⁷ m, not 500 m.
Worked example
Problem: Find photon energy for 500 nm light; h = 6.626×10⁻³⁴ J·s and c = 2.998×10⁸ m/s.
Step-by-step solution: λ = 5.00×10⁻⁷ m; E = hc/λ = 3.97×10⁻¹⁹ J per photon.
Check the units and whether the answer is reasonable before continuing.
More applications of this mathematics
Try each extension before expanding its solution.
Frequency and wavelength
For λ = 600 nm = 6.00×10⁻⁷ m, ν = c/λ ≈ 5.00×10¹⁴ Hz.
Energy per mole of photons
A photon carrying 3.0×10⁻¹⁹ J corresponds to (3.0×10⁻¹⁹ J)(6.022×10²³ mol⁻¹) ≈ 1.8×10⁵ J/mol photons.
de Broglie matter waves
An electron (mass 9.109×10⁻³¹ kg) moving at 2.00×10⁶ m/s has wavelength λ=h/(mv)=3.64×10⁻¹⁰ m using h=6.626×10⁻³⁴ J·s.
Hydrogen atom energy levels
For absorption from n=2 to n=3, ΔE=−2.178×10⁻¹⁸ J(1/3²−1/2²)=+3.03×10⁻¹⁹ J. An absorbed photon has positive energy change for the atom.
Independent practice — five questions
Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.
Supporting reference
OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.
IntoChemistry original instructional content, 2026. Formative feedback is not an official course grade. Sources are linked for independent reading. Accessibility testing with your institution and assistive technology is still recommended.