Worksheet: The Quantization of Electromagnetic Radiation

In this worksheet, we will practice calculating the energy of a photon given its frequency or wavelength.

Q1:

A laser emits 4×10 photons, each with a frequency of 6×10 Hz. What is the total energy radiated by the laser? Use a value of 6.63×10 J⋅s for the Planck constant. Give your answer in joules to 3 significant figures.

Q2:

Which of the following is the correct formula for the energy of a photon given its frequency, where represents the Planck constant and 𝑐 represents the speed of light?

  • A𝐸=𝑐𝑓
  • B𝐸=𝑓
  • C𝐸=𝑓
  • D𝐸=𝑐𝑓
  • E𝐸=𝑓

Q3:

What is the difference in the energy of a 2×10 Hz photon and a 5×10 Hz photon? Use a value of 6.63×10 J⋅s for the value of the Planck constant. Give your answer in joules to 3 significant figures.

  • A3.45×10 J
  • B6.24×10 J
  • C3.18×10 J
  • D3.32×10 J
  • E1.33×10 J

Q4:

What is the wavelength of a photon that has an energy of 2.97×10 J? Use 6.63×10 J⋅s for the value of the Planck constant and 3.00×10 m/s for the value of the speed of light in free space. Give your answer in meters to 3 significant figures.

  • A6.70×10 m
  • B1.49×10 m
  • C36.2×10 m
  • D9.98×10 m
  • E3.24×10 m

Q5:

What is the energy of a photon that has a wavelength of 400 nm? Use a value of 6.63×10 J⋅s for the value of the Planck constant and 3.00×10 m/s for the value of the speed of light in free space. Give your answer in joules to 3 significant figures.

  • A1.99×10 J
  • B6.23×10 J
  • C1.66×10 J
  • D4.97×10 J
  • E4.98×10 J

Q6:

Photon 𝐴 has twice the frequency of photon 𝐵. What is the ratio of the energy of photon 𝐴 to the energy of photon 𝐵?

Q7:

Photon A has a wavelength that is four times that of photon B. What is the ratio of the energy of photon A to the energy of photon B?

  • A2
  • B14
  • C12
  • D4
  • E1

Q8:

What is the frequency of a photon that has an energy of 2.52×10 J? Use a value of 6.63×10 J⋅s for the value of the Planck constant. Give your answer in hertz to 3 significant figures.

  • A1.90×10 Hz
  • B3.80×10 Hz
  • C1.1×10 Hz
  • D2.63×10 Hz
  • E1.95×10 Hz

Q9:

What is the difference in the energy of a blue photon, with a wavelength of 400 nm, and a red photon, with a wavelength of 700 nm? Use a value of 6.63×10 J⋅s for the value of the Planck constant and 3.00×10 m/s for the value of the speed of light in free space. Give your answer in joules to 3 significant figures.

  • A4.97×10 J
  • B2.13×10 J
  • C4.32×10 J
  • D2.84×10 J
  • E3.25×10 J

Q10:

What is the frequency of a photon that has an energy of 3.00 eV? Use 4.14×10 eV⋅s for the value of the Planck constant. Give your answer in hertz to 3 significant figures.

  • A6.98×10 Hz
  • B1.38×10 Hz
  • C3.25×10 Hz
  • D7.25×10 Hz
  • E5.32×10 Hz

Q11:

What is the energy of a photon that has a frequency of 5×10 Hz? Use 4.14×10 eV⋅s for the value of the Planck constant. Give your answer in electron volts to 3 significant figures.

Q12:

What is the energy of a photon that has a frequency of 5.50×10 Hz? Use a value of 6.63×10 J⋅s for the value of the Planck constant. Give your answer in joules to 3 significant figures.

  • A1.33×10 J
  • B8.30×10 J
  • C1.21×10 J
  • D3.65×10 J
  • E1.53×10 J

Q13:

A laser emits light with a wavelength of 200 nm. How many photons must be emitted by the laser for the amount of energy emitted to be 1 J? Use a value of 6.63×10 J⋅s for the value of the Planck constant and 3.00×10 m/s for the value of the speed of light in free space. Give your answer to 3 significant figures.

  • A8.32×10
  • B3.2×10
  • C1.36×10
  • D1.01×10
  • E9.95×10

Q14:

In this question, use a value of 6.63×10 J⋅s for the Planck constant.

A gamma ray typically has a frequency of around 3×10 Hz. Using this value, find the energy of a gamma-ray photon. Give your answer, in joules, to 3 significant figures.

  • A3.22×10 J
  • B1.99×10 J
  • C5.03×10 J
  • D1.25×10 J
  • E5.36×10 J

A radio wave typically has a frequency of around 1.5×10 Hz. Using this value, find the energy of a radio-wave photon. Give your answer in joules to 3 significant figures.

  • A9.95×10 J
  • B1.00×10 J
  • C3.25×10 J
  • D2.35×10 J
  • E7.36×10 J

How many times more energetic is a gamma-ray photon of the given frequency than a radio-wave photon of the given frequency?

  • A8.03×10
  • B5.06×10
  • C3.22×10
  • D2.00×10
  • E3.23×10

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