Plain-English Meaning
Light comes in packets called photons. Each photon's energy depends only on its colour (frequency). Violet light photons have more energy than red — which is why UV light can cause sunburn but red light cannot. h ≈ 6.63 × 10⁻³⁴ J·s is Planck's constant.
When a quantum question feels ambiguous, translating it into state, observable, probability, and evolution language usually clarifies the answer.
Deeper Explanation
E = hν = hc/λ = ℏω. For the photoelectric effect: KE_max = hν − φ (where φ is the work function). For X-rays: λ_min = hc/eV (determined by accelerating voltage). In spectroscopy, photon energy matches energy level differences: ΔE = hν.
Worked Example
Problem: A photon of visible light has wavelength 500 nm. Find its energy in eV.
- E = hc/λ
- h = 6.626×10⁻³⁴ J·s, c = 3×10⁸ m/s, λ = 500×10⁻⁹ m
- E = (6.626×10⁻³⁴ × 3×10⁸)/500×10⁻⁹ = 3.976×10⁻¹⁹ J
- Convert: E = 3.976×10⁻¹⁹ / 1.6×10⁻¹⁹ = 2.485 eV
Result: E ≈ 2.49 eV (green visible photon)
At A Glance
Category: Quantum
Levels covered: High School, College, Masters, PhD
Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.