Chemistry / Unit 5 Chem 0770 worked example, 60 to 90 seconds
Solving c = λν for Wavelength
The idea
Solving the relation c = λν for wavelength means dividing the fixed speed of light by a wave's known frequency, the mirror operation of solving for frequency.
In practice
A radio station broadcasts at a frequency ν of 1.05 × 10⁸ Hz, and the goal is its wavelength λ in meters. Substituting directly into λ = c / ν gives λ = (2.998 × 10⁸ m/s) / (1.05 × 10⁸ Hz). Since hertz is 1/s, the seconds cancel, leaving units of meters. Carrying out the division gives λ ≈ 2.85 m. Checking the result: FM radio towers are typically a few meters tall to match wavelengths in this range, so 2.85 m is a physically sensible answer, not an atomic-scale or continent-scale distance.
Where people slip
Dividing frequency by the speed of light, instead of the speed of light by frequency, inverts the answer entirely.
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