Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Blackbody Radiation and Photon Energy

Q1:

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 8 m will increase to 1 . 5 0 0 × 1 0 1 1 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.

Q2:

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?

Q3:

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

  • A Hz
  • B Hz
  • C Hz
  • D Hz
  • E Hz

Q4:

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 8 . 5 0 × 1 0 1 9 J to 4 . 2 5 × 1 0 1 9 J
  • B 6 . 3 0 × 1 0 1 9 J to 3 . 1 5 × 1 0 1 9 J
  • C 4 . 0 0 × 1 0 1 9 J to 2 . 0 1 × 1 0 1 9 J
  • D 5 . 1 0 × 1 0 1 9 J to 2 . 5 8 × 1 0 1 9 J
  • E 5 . 0 0 × 1 0 1 9 J to 2 . 3 0 × 1 0 1 9 J

Q5:

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.

Q6:

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 .

  • A4.95%
  • B0.858%
  • C0.683%
  • D0.863%
  • E4.82%

Q7:

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

What was the minimum power output during the flash?

Q8:

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?

Q9:

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 5 . 7 × 1 0 7 kW/m2
  • C 3 . 4 × 1 0 7 kW/m2
  • D 2 . 3 × 1 0 7 kW/m2
  • E 1 . 2 × 1 0 7 kW/m2

Q10:

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

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?

Q11:

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 . 1 4 × 1 0 1 5 eV⋅s for the value of the Planck Constant.

  • A 1 . 2 2 × 1 0 1 5 Hz
  • B 2 . 1 1 × 1 0 1 5 Hz
  • C 4 . 3 0 × 1 0 1 5 Hz
  • D 7 . 3 9 × 1 0 1 5 Hz
  • E 9 . 3 6 × 1 0 1 5 Hz

Q12:

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 . 0 8 6 × 1 0 1 4 W/m3
  • B 7 . 0 2 0 × 1 0 1 4 W/m3
  • C 7 . 1 7 0 × 1 0 1 4 W/m3
  • D 7 . 1 2 2 × 1 0 1 4 W/m3
  • E 7 . 2 0 1 × 1 0 1 4 W/m3