09 Worked examples (Lesson 1)
Example 1.1 — Wien's law. A star's radiation has its maximum intensity at λ = 400 nm. Using the Sun (T = 6000 K, λmax = 500 nm) as reference, estimate the star's surface temperature. λ₁T₁ = λ₂T₂ → 500 × 6000 = 400 × T₂ → T₂ = 7500 K. The star is hotter than the Sun, so its peak is at a shorter wavelength, as expected.
Example 1.2 — Energy of an emitted photon. An oscillating atom in a hot body drops from one allowed level to the next and emits radiation of frequency 5.0 × 10¹⁴ Hz. Find the energy of the emitted photon in joules and in eV. E = hν = 6.63 × 10⁻³⁴ × 5.0 × 10¹⁴ = 3.32 × 10⁻¹⁹ J. In eV: 3.32 × 10⁻¹⁹ / 1.6 × 10⁻¹⁹ = 2.07 eV. (λ = c/ν = 600 nm: orange light.)
Example 1.3 — Photons per second. A 40 W lamp turns 5 % of its power into visible light of average wavelength 550 nm. How many photons per second does it emit? Visible power = 0.05 × 40 = 2 W. Energy of one photon = hc/λ = 1.99 × 10⁻²⁵ / 5.5 × 10⁻⁷ = 3.62 × 10⁻¹⁹ J. Rate = 2 / 3.62 × 10⁻¹⁹ = 5.5 × 10¹⁸ photons per second.