Topic 15.4 Blackbody Radiation: describe the thermal radiation spectrum of a hot object and how its peak shifts with temperature.

What this topic is asking

The College Board (Topic 15.4) wants you to describe blackbody radiation: the thermal radiation spectrum of a hot object, how its peak wavelength shifts to shorter wavelengths as temperature rises, how the total power grows, and why quantisation was needed to explain it.

What blackbody radiation is

Any object above absolute zero radiates electromagnetic energy simply because of its temperature, the random thermal motion of its charges. The radiation spans a continuous range of wavelengths (unlike the discrete line spectra of Topic 15.2), with a smooth peak. At room temperature the peak is in the infrared (invisible), which is why a warm object does not glow visibly; heat it enough and the peak moves into the visible range and it begins to glow.

How the spectrum changes with temperature

Two trends define the temperature dependence. First, the color shift: the hotter the object, the shorter its peak wavelength, so the glow moves from red toward blue. Second, the brightness surge: total radiated power climbs steeply with temperature, so a small temperature rise greatly increases the energy output. Together these let astronomers read a star's temperature from its color and brightness, and they explain everyday observations like a stove element glowing red while a far hotter filament glows white.

Why classical physics failed, and quantisation

The blackbody spectrum was a crisis for classical physics. Wave theory predicted that the radiation should grow without limit at short wavelengths, the ultraviolet catastrophe, which is absurd (an object would radiate infinite energy). Planck solved it by assuming energy is exchanged only in discrete quanta of size $E = hf$. Because high-frequency (short-wavelength) photons are energetic and hard to excite thermally, this quantisation suppresses the short-wavelength radiation, giving a spectrum that peaks and falls off, exactly matching experiment. The strategic role of this topic is historic and conceptual: blackbody radiation was the first evidence that energy is quantised, the seed of the photon idea (Topic 15.1) later confirmed by the photoelectric effect (Topic 15.5). It connects the thermal physics of Unit 9 (hot objects) to the quantum physics of this unit, showing that even the glow of a hot object demands $E = hf$.

Try this

Q1. State what happens to the peak wavelength of a blackbody as its temperature increases. [1 point]

• Cue. It shifts to shorter wavelengths (toward blue).

Q2. State what classical physics wrongly predicted about blackbody radiation, and what fixed it. [2 points]

• Cue. It predicted unlimited radiation at short wavelengths (the ultraviolet catastrophe); quantising energy into photons of $E = hf$ fixed it.