Black Body Radiation: 18 MCQs with answers

An idealized object that absorbs all incident electromagnetic radiation

A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.

It emits radiation with a spectrum that depends only on its temperature

A black body emits radiation across all wavelengths, and the spectral distribution depends solely on its temperature, as described by Planck's law.

Absorbs all incident light, making it appear black at low temperatures

At low temperatures, a perfect absorber would not reflect any light, so it would appear black. Hence the name 'black body'.

The temperature of the body

The black body spectrum is universal and depends only on the temperature, not on the material or shape.

Stefan-Boltzmann law

The Stefan-Boltzmann law states that the total energy radiated per unit surface area is proportional to the fourth power of the temperature (E = σT⁴).

Decreases

Wien's law states that the peak wavelength is inversely proportional to temperature (λ_max = b/T), so higher temperature means shorter peak wavelength.

1

A perfect black body has an emissivity of 1, meaning it emits the maximum possible radiation at its temperature.

True

By definition, a black body is a perfect absorber of all incident radiation.

False

The spectrum depends only on temperature, not on the material.

2.9 × 10⁻³ m·K

Wien's displacement constant is approximately 2.9 × 10⁻³ m·K.

Planck's law

Planck's law gives the intensity of radiation emitted at each wavelength for a given temperature, accurately describing the black body spectrum.

Rayleigh-Jeans law

The Rayleigh-Jeans law predicted infinite energy at short wavelengths, leading to the ultraviolet catastrophe, which was resolved by Planck's quantum hypothesis.

That energy is emitted or absorbed in discrete quanta

Planck proposed that electromagnetic energy is quantized, emitted or absorbed in discrete packets (quanta) proportional to frequency (E = hν).

Its emission spectrum depends on its material

A black body's emission spectrum is independent of material; it depends only on temperature.

5.67 × 10⁻⁸ W/m²K⁴

The Stefan-Boltzmann constant is approximately 5.67 × 10⁻⁸ W/m²K⁴.

16

According to the Stefan-Boltzmann law (E ∝ T⁴), doubling T increases E by 2⁴ = 16 times.

Infrared

At room temperature (~300 K), Wien's law gives a peak wavelength around 10 μm, which is in the infrared region.

A small hole in a cavity

A small hole in a cavity acts as a black body because any radiation entering the hole is absorbed after multiple reflections, and the emitted radiation depends only on the cavity's temperature.