Explicit science instruction
Electromagnetic waves satisfy c = λν. For light in vacuum, c = 3.00×10⁸ m/s. Convert nanometers to meters before substitution: 1 nm = 1×10⁻⁹ m.
Photon energy is E = hν. Higher frequency therefore means higher photon energy. Since wavelength and frequency are inversely related, shorter wavelength corresponds to higher photon energy.
Vocabulary: wavelength; frequency; speed of light; photon energy; inverse relationship.
Worked example with reasoning
For λ=500 nm, λ=5.00×10⁻⁷ m. Then ν=(3.00×10⁸)/(5.00×10⁻⁷)=6.00×10¹⁴ Hz. A 400 nm photon therefore has higher energy than a 700 nm photon.
Guided question
Calculate frequency for 600 nm light and show the wavelength conversion.
Independent work
- Calculate frequencies for 400, 500, and 750 nm.
- Rank their photon energies.
- Describe one unit-conversion error that would change the answer by orders of magnitude.
Misconception check
Longer wavelength does not mean higher photon energy; wavelength and frequency are inversely related.
Formative understanding check
Which has greater photon energy, 450 nm or 650 nm light?
Reveal response
450 nm light because it has higher frequency.
Mentor evidence conference
Ask Archaemenes to audit your powers of ten and unit cancellation.
Teacher guidance
Foundation: Convert nm to m and identify the inverse relationship.
Core: Calculate frequency and rank photon energies.
Extended: Use E=hν with a supplied Planck constant.
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