Worksheet: Blackbody Radiation

In this worksheet, we will practice describing the change with temperature of an ideal blackbody's color and explaining how this shows the quantization of light.

Q1:

The total energy emitted by a black body is 1.25 µJ. If the total radiated energy is divided into quanta with a wavelength of 700 nm, how many such quanta would be emitted? Use 6.626×10 J⋅s for the value of Planck’s constant. Answer in scientific notation to two decimal places.

  • A8.05×10
  • B1.15×10
  • C1.06×10
  • D6.12×10
  • E4.40×10

Q2:

Pick the word that would correctly complete the following statement about the absorption of electromagnetic radiation by an ideal black body:

The part of the absorption spectrum of an ideal black body containing the greater range of wavelengths contains wavelengths than the wavelength that is most strongly absorbed by the black body.

  • Alonger
  • Bshorter

Q3:

Which word would correctly complete the following statement about the resonant modes of electromagnetic waves in a cavity?

An electromagnetic wave that is a resonant mode for a cavity must have displacement at the cavity boundaries.

  • Azero
  • Bmaximum
  • Cnonzero

Q4:

Pick the word that would correctly complete the following statement about the emission of electromagnetic radiation by an ideal black body:

The electromagnetic-radiation-emission spectrum of an ideal black body is the spectrum of the radiation that the black body absorbs.

  • Aindependent of
  • Bthe same as
  • Cthe inverse of

Q5:

Which of the electromagnetic waves shown in the diagram of a cavity corresponds to a possible resonant mode of the cavity?

  • A
  • B

Q6:

Which of the electromagnetic waves shown in the diagram of a cavity corresponds to a possible resonant mode of the cavity?

  • A
  • B
  • C

Q7:

The diagrams (a), (b), and (c) show the possible resonant cavity modes for electromagnetic waves that are emitted from a point in a cavity. Considering the wavelength of a wave that can form a resonant cavity mode and the number of modes with that wavelength that can exist in a particular cavity, would increasing the wavelength increase, decrease, or not affect the number of modes?

  • AIncrease
  • BDecrease
  • CNo effect

Q8:

Which of the electromagnetic waves shown in the diagram of a cavity corresponds to a possible resonant mode of the cavity?

  • A
  • B

Q9:

Using the Rayleigh–Jeans law of black-body radiation, calculate the intensity of electromagnetic radiation with a wavelength of 700 nm emitted by a black body with a temperature of 2,500 K. Use 1.3806×10 m2⋅kg/s2⋅K for the value of Boltzmann’s constant. Answer in scientific notation to two decimal places.

  • A2.71×10 W/m2
  • B8.04×10 W/m2
  • C5.90×10 W/m2
  • D1.15×10 W/m2
  • E8.39×10 W/m2

Q10:

The diagram shows a curve that represents the electromagnetic radiation–emission spectrum of a black body that has a peak wavelength 𝜆.

Which words would correctly complete the following statement about the reasons for the shape of the spectrum?

In region of the spectrum, the change in intensity of emitted radiation with a wavelength of emitted radiation is mostly because the light quanta with wavelengths in this region take up a portion of the total energy emitted by the black body than the light quanta with the wavelengths found in region .

  • AI, smaller, II
  • BII, smaller, I
  • CII, larger, I
  • DI, larger, II

Which words would correctly complete the following statement about the reasons for the shape of the spectrum?

In region of the spectrum, the change in intensity of emitted radiation with a wavelength of emitted radiation is mostly due to the number of resonant modes of each wavelength as the wavelength decreases.

  • AI, decreasing
  • BII, decreasing
  • CII, increasing
  • DI, increasing

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