Wien’s displacement law tells us how the peak wavelength of a star’s light depends on its surface temperature.
Think of a star as a giant oven: the hotter it is, the more it glows blue (short wavelengths) and the less it glows red (long wavelengths). 🌞🔥
\$\lambda_{\text{max}} = \frac{b}{T}\$
where
\$b \approx 2.898 \times 10^{-3}\,\text{m·K}\$
(the Wien constant).
Key point: λmax is inversely proportional to T.
\$T = \frac{2.898 \times 10^{-3}\,\text{m·K}}{5 \times 10^{-7}\,\text{m}} \approx 5.8 \times 10^{3}\,\text{K}\$
≈ 5800 K.
| Star Type | λmax (nm) | T (K) |
|---|---|---|
| O‑type (blue) | 100 nm | ≈ 30 000 K |
| A‑type (white) | 400 nm | ≈ 9 000 K |
| K‑type (orange) | 700 nm | ≈ 5 000 K |
| M‑type (red) | 1 200 nm | ≈ 3 000 K |
Exam Tip:
• If you’re given λmax, use \$T = \frac{b}{\lambda_{\text{max}}}\$.
• If you’re given T, find λmax with \$\lambda_{\text{max}} = \frac{b}{T}\$.
• Remember the units: λmax in metres, T in kelvin, b in m·K.
• A quick mental check: hotter stars → shorter λmax (blue), cooler stars → longer λmax (red).
❓ Practice with a few different star types to get comfortable!