Preview

Blackbody Spectrum

Q: The Sun's surface is ~5778K. What is its peak emission wavelength?

Λ_max = 2.898×10⁻³ / 5778 ≈ 501.5 nm — green visible light.

Q: At what temperature does an object peak in the visible range (~550nm)?

You can work it out this way: solve Wien's Law for T: T = b/λ_max ≈ 5269 K.

Q: How much more power does a 6000K star emit compared to a 3000K star?

P ∝ T⁴; ratio = (6000/3000)⁴ = 16.

Explore thermal radiation and the quantum revolution

Every language has the same color code: red means hot, blue means cool. Faucets, weather maps, chili sauce. Physics disagrees — completely. Heat a bar of iron and it glows red first BECAUSE red is the coolest glow there is; push the temperature and the glow climbs through orange and yellow to blue-white fury. The rule underneath is Wien's displacement law, λ_max = b/T: every warm object emits a full Planck spectrum whose peak slides to shorter wavelengths as temperature rises. In nature, as the astronomy textbook puts it, the art-class color code runs 'the other way around'. That one law lets astronomers take a star's temperature from its color alone — no thermometer, no visit. And riding along is a second law with a temper: total power grows as T⁴, so doubling the temperature multiplies the output sixteen-fold. This curve carries one more distinction: classical physics predicted it should soar to infinity in the ultraviolet, and it doesn't. Max Planck fixed the books on December 14, 1900 by proposing that energy moves only in discrete quanta, E = hf — a 'mathematical trick' that turned out to be the birth of quantum mechanics. In this lab you'll slide one temperature knob from a room-warm 300 K (you, glowing invisibly at 9.7 microns — exactly where thermal cameras look) through the Sun's green-peaked 5778 K to a blue star's 20000 K, and watch the peak march blueward, the power explode, and the everyday color code fail on schedule.

What you'll be able to do

Apply Wien's law λ_max = b/T across three worlds on the panel: the Sun's 5778 K peaks at 501.5 nm (green, visible), a 20000 K blue star at 144.9 nm (ultraviolet — the visible blue-white is the curve's tail), and a 300 K room at 9659 nm (deep infrared, the ~9.5 μm band thermal cameras image) — hotter is always bluer, never redder
Apply Stefan-Boltzmann P = σT⁴ quantitatively: doubling 6000 → 12000 K multiplies the Total Power row by exactly 2⁴ = 16 (7.35×10⁷ → 1.18×10⁹ W/m²), and the slider's own bookends land the law's signature — a hundredfold temperature span (300 → 30000 K) spans 10⁸ in power (4.59×10² → 4.59×10¹⁰ W/m²)
Read the Planck curve as the birth certificate of quantum mechanics: the machine-verified peak radiance (2.64×10¹³ W/m²/sr/m at solar temperature) sits exactly where classical physics predicted infinity — Planck's quanta E = hf make high-frequency modes exponentially unlikely, cutting off the ultraviolet catastrophe (quiz Q3), and the same curve at 2.725 K is the cosmic microwave background

Formulas

B(\lambda,T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{hc/\lambda k_B T} - 1}

Planck spectral radiance — energy per area, solid angle, and wavelength

\lambda_{max} = \frac{b}{T}

Wien's Displacement Law (b = 2.898×10⁻³ m·K)

P = \sigma A T^4

Stefan-Boltzmann Law (σ = 5.67×10⁻⁸ W/m²/K⁴)

Make a prediction

Sun Surface default: T = 5778 K, the spectrum peaks at 501.5 nm — visible green — and Total Power reads 6.32×10⁷ W/m². Now crank the temperature to 20000 K (the Blue Star preset). Where does the spectral peak go?

No grading here — commit to a guess, then scroll down and test it yourself.

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Explore

Run the gate live: hit Blue Star (20000 K) and watch three things at once — λ_max slides 501.5 → 144.9 nm, the Color Region row flips Visible → Ultraviolet, and the glowing sphere turns blue-white. Hotter is bluer. Every time, no exceptions.
Visit your own glow: Room Temp (300 K) parks the peak at 9659 nm — deep infrared, almost exactly the 9.5 μm band thermal cameras image. The window widens to 30 μm to catch it, and the visible band holds nothing at all: you glow constantly, just not in light you can see.
Audit the T⁴ ledger: set 6000 K and read the power (7.35×10⁷ W/m²), then double to 12000 K — 1.18×10⁹, exactly sixteen-fold. Then check the slider's own bookends: 300 K reads 4.59×10², 30000 K reads 4.59×10¹⁰ — same mantissa, eight orders apart, the fourth power's signature.
Work the λ Window like an astronomer: at Blue Star, narrow it to 1 μm and the whole story fits; at Room Temp, stretch it to 30 μm or the peak lives outside your instrument. Choosing the observation window IS part of reading a spectrum.

Scroll for the debrief ↓

Check

Did the lab agree with you?

Your prediction

You skipped the prediction — jump back to the preview and commit to a guess first; the comparison is the whole point.

Answer: It slides to 144.9 nm — into the ULTRAVIOLET: hotter is bluer (λ_max = b/T), the visible blue-white is just the curve's tail, and the power explodes ×143 (T⁴)

Wien's law is an inverse law: λ_max = b/T, so more temperature means a SHORTER peak wavelength — 2.898×10⁻³/20000 = 144.9 nm, deep in the ultraviolet, and the panel's Color Region row flips from Visible to Ultraviolet. 'The hotter the body, the shorter the wavelength corresponding to the emission peak' (OpenStax, verbatim). Option B is the everyday color code — and the astronomy textbook names it directly: 'In art, red is often called a hot color and blue a cool color… in nature, it's the other way around.' Red-hot iron glows red because it's at the COOL end of glowing (~1000–1500 K); the Sun's peak is already green, and hotter stars are blue-white because their peaks have left the visible band on the blue side. Option C is the sim's own flagged misconception — the curve does grow (spectacularly: ×143 in total power, by T⁴), but it never grows in place: the entire distribution marches blueward as it rises. Watch the amber Wien marker — it cannot stay put.

Quiz (0/3)

The Sun's surface is ~5778K. What is its peak emission wavelength?

At what temperature does an object peak in the visible range (~550nm)?

How much more power does a 6000K star emit compared to a 3000K star?

You can now

Apply Wien's law λ_max = b/T across three worlds on the panel: the Sun's 5778 K peaks at 501.5 nm (green, visible), a 20000 K blue star at 144.9 nm (ultraviolet — the visible blue-white is the curve's tail), and a 300 K room at 9659 nm (deep infrared, the ~9.5 μm band thermal cameras image) — hotter is always bluer, never redder
Apply Stefan-Boltzmann P = σT⁴ quantitatively: doubling 6000 → 12000 K multiplies the Total Power row by exactly 2⁴ = 16 (7.35×10⁷ → 1.18×10⁹ W/m²), and the slider's own bookends land the law's signature — a hundredfold temperature span (300 → 30000 K) spans 10⁸ in power (4.59×10² → 4.59×10¹⁰ W/m²)
Read the Planck curve as the birth certificate of quantum mechanics: the machine-verified peak radiance (2.64×10¹³ W/m²/sr/m at solar temperature) sits exactly where classical physics predicted infinity — Planck's quanta E = hf make high-frequency modes exponentially unlikely, cutting off the ultraviolet catastrophe (quiz Q3), and the same curve at 2.725 K is the cosmic microwave background