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Quantum Formula

What is Planck's Relation?

Energy is quantised — photon energy is proportional to frequency.

Formula: E = h\nu

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.