---
title: "Wien's Law — AP Physics 2 Definition & Exam Guide"
description: "Wien's law (λmax = b/T) says hotter blackbodies peak at shorter wavelengths. Learn how it pairs with Stefan-Boltzmann ratios on AP Physics 2 Unit 15 questions."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/wiens-law"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 15"
---

# Wien's Law — AP Physics 2 Definition & Exam Guide

## Definition

Wien's law states that the peak wavelength of a blackbody's emission spectrum is inversely proportional to its absolute temperature, λmax = b/T, so hotter objects radiate most intensely at shorter wavelengths (think red-hot vs. white-hot).

## What It Is

Wien's law tells you where a [blackbody](/ap-physics-2-revised/unit-15/4-blackbody-radiation/study-guide/jcWRJUVghpDEK71c "fv-autolink")'s radiation curve peaks. A blackbody is an idealized object that absorbs all radiation hitting it, and when it sits in equilibrium at some temperature, it emits a [continuous spectrum](/ap-physics-2-revised/key-terms/continuous-spectrum "fv-autolink") that depends only on that temperature. Plot intensity per unit wavelength versus wavelength and you get a hump-shaped curve. Wien's law locates the top of that hump: λmax = b/T, where b is Wien's constant (about 2.9 × 10⁻³ m·K) and T is the absolute temperature in kelvins.

The relationship is a pure inverse proportion. Double the temperature and the peak wavelength gets cut in half. That's why a heating element glows dull red at lower temperatures but a hotter star like the Sun peaks in the visible range, and an even hotter star looks blue-white. The peak slides toward shorter wavelengths as T climbs. Wien's law describes one feature of the curve (where the peak sits), not the whole curve. Describing the full shape of the spectrum is Planck's job, and that's exactly where classical physics broke down.

## Why It Matters

Wien's law lives in Topic 15.4 (Blackbody Radiation) in [Unit 15](/ap-physics-2-revised/unit-15 "fv-autolink"): Modern Physics, supporting learning objective 15.4.A, which asks you to describe the [electromagnetic radiation](/ap-physics-2-revised/key-terms/electromagnetic-radiation "fv-autolink") an object emits because of its temperature. The CED's essential knowledge spells out the setup. Matter spontaneously converts internal thermal energy into electromagnetic energy, a blackbody in equilibrium emits a continuous spectrum that depends only on temperature, and that spectrum gets modeled as intensity per unit wavelength versus wavelength. Wien's law is the quantitative handle on that graph. It's also part of the historical punchline of Unit 15: classical physics could not explain the blackbody spectrum's shape, and resolving that failure launched quantum physics. Knowing what the curve does as temperature changes is the foundation for understanding why Planck's quantum hypothesis was needed at all.

## Connections

### [Stefan-Boltzmann law (Unit 15)](/ap-physics-2-revised/key-terms/stefan-boltzmann-law)

These two laws answer different questions about the same blackbody. Wien's law tells you WHERE the spectrum peaks (λmax = b/T), while Stefan-Boltzmann tells you HOW MUCH total power gets radiated (proportional to T⁴). Exam questions love combining them: double the [temperature](/ap-physics-2-revised/unit-9/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3 "fv-autolink") and the peak wavelength halves, but the power jumps by a factor of 16.

### [Planck's law (Unit 15)](/ap-physics-2-revised/key-terms/plancks-law)

[Planck's law](/ap-physics-2-revised/key-terms/plancks-law "fv-autolink") gives the full shape of the blackbody curve at every wavelength; Wien's law is just the location of that curve's maximum. Historically, classical physics couldn't reproduce the curve's shape, and Planck fixed it by quantizing energy, which is the opening move of all of modern physics.

### [Continuous spectrum (Unit 15)](/ap-physics-2-revised/key-terms/continuous-spectrum)

A blackbody emits a continuous spectrum, meaning all wavelengths are present with no gaps. Wien's law only makes sense because of this. There's a smooth curve of [intensity](/ap-physics-2-revised/key-terms/intensity "fv-autolink") across wavelengths, and Wien picks out the single wavelength where that smooth curve tops out. Contrast this with the discrete line spectra atoms emit, which come from quantized energy levels.

### Electromagnetic waves (Unit 14)

Blackbody radiation IS electromagnetic radiation, so Wien's law connects temperature to a spot on the EM spectrum you studied earlier. A 6000 K object peaks in [visible light](/ap-physics-2-revised/unit-14/4-electromagnetic-waves/study-guide/hZjkcwjYXeKC1jmo "fv-autolink"), while a room-temperature object peaks in the infrared, which is why you can't see thermal radiation from everyday objects but an IR camera can.

## On the AP Exam

Wien's law shows up mostly as ratio reasoning, not plug-and-chug with the constant b. A classic stem gives you two blackbodies, say 3000 K and 6000 K, and asks how their peak wavelengths compare. Since λmax ∝ 1/T, doubling the temperature halves the peak wavelength. The trap is that these questions almost always bundle in Stefan-Boltzmann too, asking for the ratio of total radiated powers in the same breath. Keep the two relationships straight: peak wavelength scales as 1/T, total power scales as T⁴. So going from T to 2T means λmax drops by half while power multiplies by 16. You may also need to interpret intensity-versus-wavelength graphs, identifying which curve belongs to the hotter object (higher peak, shifted left) and explaining qualitatively why the peak moves. No released FRQ has hinged on Wien's law verbatim, but it supports any free-response prompt asking you to describe how a blackbody's emission changes with temperature under LO 15.4.A.

## Wien's law vs Stefan-Boltzmann law

Both describe blackbody radiation as a function of temperature, so they get scrambled constantly. Wien's law is about the peak wavelength and goes as 1/T (an inverse first-power relationship). Stefan-Boltzmann is about total radiated power and goes as T⁴. If a question asks 'what color' or 'what wavelength,' that's Wien. If it asks 'how much energy per second,' that's Stefan-Boltzmann. When temperature doubles, the answers diverge dramatically: wavelength halves, power goes up 16-fold.

## Key Takeaways

- Wien's law says λmax = b/T, so the peak wavelength of a blackbody's spectrum is inversely proportional to its absolute temperature.
- Hotter objects peak at shorter wavelengths, which is why objects shift from red-hot to white-hot to blue-white as temperature rises.
- Doubling the temperature cuts the peak wavelength in half, but it multiplies the total radiated power by 16 because of the Stefan-Boltzmann T⁴ law.
- A blackbody's continuous spectrum depends only on its temperature, and Wien's law identifies the single wavelength where intensity per unit wavelength is greatest.
- On a graph of intensity versus wavelength, the hotter blackbody's curve is taller everywhere and its peak sits farther left (shorter wavelength).
- Temperature must be in kelvins; Wien's law uses absolute temperature, never Celsius.

## FAQs

### What is Wien's law in AP Physics 2?

Wien's law states that the wavelength at which a blackbody emits most intensely is inversely proportional to its absolute temperature: λmax = b/T, with b ≈ 2.9 × 10⁻³ m·K. It's tested in Topic 15.4 (Blackbody Radiation) under learning objective 15.4.A.

### Does Wien's law say hotter objects emit longer wavelengths?

No, it's the opposite. Hotter objects peak at SHORTER wavelengths because λmax ∝ 1/T. A 6000 K blackbody peaks at half the wavelength of a 3000 K blackbody, which is why hotter stars look blue-white instead of red.

### What's the difference between Wien's law and the Stefan-Boltzmann law?

Wien's law gives the peak wavelength of the emission spectrum (λmax = b/T), while Stefan-Boltzmann gives the total power radiated (proportional to T⁴). Wien answers 'what wavelength dominates,' Stefan-Boltzmann answers 'how much total energy per second.'

### What happens to the peak wavelength if a blackbody's temperature doubles?

The peak wavelength is cut in half, since λmax ∝ 1/T. For example, going from 2000 K to 4000 K halves λmax, and the same temperature jump multiplies the total radiated power by 2⁴ = 16.

### Is Wien's law the same as Planck's law?

No. Planck's law describes the entire blackbody intensity curve across all wavelengths, while Wien's law only pinpoints where that curve peaks. You can think of Wien's law as one feature you can read off the full curve Planck's law generates.

## Related Study Guides

- [15.4 Blackbody Radiation](/ap-physics-2-revised/unit-15/4-blackbody-radiation/study-guide/jcWRJUVghpDEK71c)

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