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 1 0 0 0 0 K.

  • A 7 . 1 7 0 × 1 0 W/m3
  • B 7 . 2 0 1 × 1 0 W/m3
  • C 7 . 0 2 0 × 1 0 W/m3
  • D 7 . 0 8 6 × 1 0 W/m3
  • E 7 . 1 2 2 × 1 0 W/m3

Q2:

A 200-W heater emits a 1.50- 𝜇 m radiation. Radiation from the heater warms a 4.00-kg body 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?

  • A 2 . 6 × 1 0
  • B 1 . 7 × 1 0
  • C 3 . 1 × 1 0
  • D 3 . 5 × 1 0
  • E 2 . 1 × 1 0

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 to 1 0 0 C and evaporated it. Flesh has a latent heat of vaporization of 2 2 5 6 kJ/kg.

How many photons were required to vaporize the flesh?

  • A 1 . 9 8 × 1 0
  • B 2 . 1 7 × 1 0
  • C 1 . 7 6 × 1 0
  • D 1 . 1 9 × 1 0
  • E 1 . 3 4 × 1 0

What was the minimum power output during the flash?

Q4:

A photon has the same energy as a proton that is moving at 0 . 0 1 0 0 𝑐 .

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 L i 2 + ion in its first excited state if the energy required is 30.6 eV? Use a value of 4 . 1 4 × 1 0 eV⋅s for the value of the Planck Constant.

  • A 2 . 1 1 × 1 0 Hz
  • B 1 . 2 2 × 1 0 Hz
  • C 7 . 3 9 × 1 0 Hz
  • D 4 . 3 0 × 1 0 Hz
  • E 9 . 3 6 × 1 0 Hz

Q6:

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

  • A 2 . 3 6 × 1 0 Hz
  • B 6 . 0 0 × 1 0 Hz
  • C 5 . 2 7 × 1 0 Hz
  • D 7 . 2 5 × 1 0 Hz
  • E 3 . 5 0 × 1 0 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?

  • A 4 . 0 0 × 1 0 J to 2 . 0 1 × 1 0 J
  • B 8 . 5 0 × 1 0 J to 4 . 2 5 × 1 0 J
  • C 5 . 0 0 × 1 0 J to 2 . 3 0 × 1 0 J
  • D 6 . 3 0 × 1 0 J to 3 . 1 5 × 1 0 J
  • E 5 . 1 0 × 1 0 J to 2 . 5 8 × 1 0 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.

  • A 7 . 9 × 1 0 7 kW/m2
  • B 3 . 4 × 1 0 7 kW/m2
  • C 2 . 3 × 1 0 7 kW/m2
  • D 1 . 2 × 1 0 7 kW/m2
  • E 5 . 7 × 1 0 7 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 7 7 8 K, while its present radius of 6 . 9 0 0 × 1 0 m will increase to 1 . 5 0 0 × 1 0 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 9 8 . 8 F to 1 0 0 F .

  • A0.683%
  • B0.863%
  • C4.82%
  • D4.95%
  • E0.858%

Q13:

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

  • A 7 . 2 5 × 1 0 1 3 Hz
  • B 1 . 4 8 × 1 0 8 Hz
  • C 7 . 2 5 × 1 0 1 0 Hz
  • D 4 . 4 2 × 1 0 1 3 Hz
  • E 1 . 2 4 × 1 0 9 Hz

Q14:

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

  • A 10.5 kV
  • B 15.3 kV
  • C 12.8 kV
  • D 12.4 kV
  • E 11.0 kV

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