Worksheet: Blackbody Radiation and Photon Energy

In this worksheet, we will practice relating a blackbody temperature to its emitted and absorbed light wavelengths and how to relate those to photon energies.

Q1:

Determine the power intensity of radiation per unit wavelength emitted at a wavelength of 500.0 nm by a blackbody at a temperature of 10,000 K.

  • A7.020×10 W/m3
  • B7.201×10 W/m3
  • C7.170×10 W/m3
  • D7.122×10 W/m3
  • E7.086×10 W/m3

Q2:

A 200 W heater emits a 1.50 μm radiation. Radiation from the heater warms a body of mass 4.00 kg by 2.00 K.

What value of the energy quantum does it emit?

Assuming that the specific heat capacity of the body is 0.83 kcal/kg⋅K, how many photons must be absorbed to warm the body?

  • A2.6×10
  • B3.5×10
  • C2.1×10
  • D1.7×10
  • E3.1×10

Assuming that all the radiation that the heater emits is absorbed by the body, how much time is required for the body’s temperature to increase?

Q3:

Lasers can be used as surgical instruments to vaporize flesh by heating it. A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 μm. In 1.00 ms, this laser raised the temperature of 1.00 cm3 of flesh from 25C to 100C. Flesh has a latent heat of vaporization of 2,256 kJ/kg. Considering the human flesh as water, the specific heat is 4,186/JkgC and the density is 997 kg/m3.

How many photons were required to vaporize the flesh?

  • A1.19×10
  • B2.17×10
  • C1.98×10
  • D1.76×10
  • E1.37×10

What was the minimum power output during the flash?

Q4:

A photon has the same energy as a proton that is moving at 0.0100𝑐.

What is the wavelength of the photon?

What is the energy of the photon?

What is the kinetic energy of the proton?

Q5:

What is the minimum frequency of a photon required to ionize a Li2+ ion in its first excited state if the energy required is 30.6 eV? Use a value of 4.14×10 eV⋅s for the value of the Planck constant.

  • A9.36×10 Hz
  • B1.22×10 Hz
  • C7.39×10 Hz
  • D2.11×10 Hz
  • E4.30×10 Hz

Q6:

The tungsten elements of incandescent light bulbs operate at 700 K. At what frequency does the filament radiate maximum energy?

  • A7.25×10 Hz
  • B2.36×10 Hz
  • C3.50×10 Hz
  • D6.00×10 Hz
  • E5.27×10 Hz

Q7:

The radiant energy from the Sun reaches its maximum at a wavelength of about 0.5 μm. What is the approximate temperature of the Sun’s surface?

Q8:

The wavelengths of visible light range from approximately 390 nm to 770 nm. What is the corresponding range of photon energies for visible light?

  • A4.00×10 J to 2.01×10 J
  • B8.50×10 J to 4.25×10 J
  • C5.00×10 J to 2.30×10 J
  • D6.30×10 J to 3.15×10 J
  • E5.10×10 J to 2.58×10 J

Q9:

Calculate the temperature of the Sun, modeling the Sun as a black body emitting radiation at a maximum intensity at a wavelength of 0.500 micrometers.

Q10:

Calculate the heat flux emitted from the Sun’s surface, modeling the Sun as a black body emitting radiation at maximum intensity at a 0.50-micrometer wavelength.

  • A2.3×10 kW/m2
  • B7.9×10 kW/m2
  • C5.7×10 kW/m2
  • D3.4×10 kW/m2
  • E1.2×10 kW/m2

Q11:

In about five billion years, the Sun will evolve into a red giant. Assume that its surface temperature will decrease to about half its present value of 5,778 K, while its present radius of 6.900×10 m will increase to 1.500×10 m, which is the current Earth-Sun distance. Calculate the ratio of the total power emitted by the Sun in its red giant stage to its present power.

Q12:

Treating the human body as a blackbody, determine the percentage increase in the total power of its radiation when its temperature increases from 98.8F to 100F.

  • A0.683%
  • B0.863%
  • C4.82%
  • D0.858%
  • E4.95%

Q13:

The tungsten elements of incandescent light bulbs operate at 700 K. At what frequency does the filament radiate the most energy?

  • A7.25×10 Hz
  • B1.24×10 Hz
  • C7.25×10 Hz
  • D4.42×10 Hz
  • E1.48×10 Hz

Q14:

What voltage must be applied to an X-ray tube to obtain an X-ray with a wavelength of 0.100 nm?

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