Worksheet: Photons

In this worksheet, we will practice relating the energy and momentum of photons to the wavelength of electromagnetic waves consisting of such photons.

Q1:

A photon has an energy of 20.0 keV.

What is this photon’s frequency?

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

What is this photon’s wavelength?

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

Q2:

An AM radio transmitter radiates 5 . 0 0 × 1 0 W of electromagnetic radiation at a frequency of 7 . 6 0 × 1 0 Hz. How many photons per second does the transmitter emit?

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

Q3:

In the 1980s, the term picowave was used to describe food irradiation in order to overcome public resistance by playing on the well-known safety of microwave radiation. Find the energy in MeV of a photon having a wavelength of 1.00 picometer.

Q4:

What is the momentum of a 4.00-cm-wavelength photon?

  • A 1 . 2 8 × 1 0 kg⋅m/s
  • B 1 . 1 7 × 1 0 kg⋅m/s
  • C 1 . 4 1 × 1 0 kg⋅m/s
  • D 1 . 6 6 × 1 0 kg⋅m/s
  • E 1 . 5 3 × 1 0 kg⋅m/s

Q5:

During a time interval of 1.00 s, light with an intensity of 1.00 kW/m2 is incident on a mirror with an area of 2.00 m2 and is completely reflected.

What is the energy of the light reflected from the mirror?

How much momentum is imparted to the mirror?

  • A 0 . 7 0 7 × 1 0 kg⋅m/s
  • B 1 . 3 3 × 1 0 kg⋅m/s
  • C 1 . 7 1 × 1 0 kg⋅m/s
  • D 1 . 5 9 × 1 0 kg⋅m/s
  • E 1 . 0 1 × 1 0 kg⋅m/s

How much force is exerted on the mirror?

  • A 2 . 2 6 × 1 0 N
  • B 1 . 3 3 × 1 0 N
  • C 1 . 0 1 × 1 0 N
  • D 1 . 8 2 × 1 0 N
  • E 2 . 6 8 × 1 0 N

Q6:

Radiation known as the solar wind is incident on the top of Earth’s atmosphere has with average intensity of 1.30 kW/m2. Suppose that you are building a solar sail that will use the radiation pressure of the solar wind to propel a small toy spaceship with a mass of 0.100 kg. The sail is made from a material, which perfectly reflects radiation of the solar wind. To assess whether such a project is feasible, answer the following questions, assuming that radiation photons are incident only in normal direction to the sail reflecting surface.

What is the radiation pressure of the solar wind on the solar sail?

  • A 8 . 4 3 × 1 0 N/m2
  • B 8 . 6 7 × 1 0 N/m2
  • C 8 . 9 0 × 1 0 N/m2
  • D 9 . 1 9 × 1 0 N/m2
  • E 8 . 2 8 × 1 0 N/m2

How much acceleration of the toy spaceship would the solar sail produce if the sail’s area is 10.0 m2?

  • A 6 . 6 3 × 1 0 m/s2
  • B 9 . 0 3 × 1 0 m/s2
  • C 8 . 0 5 × 1 0 m/s2
  • D 7 . 3 6 × 1 0 m/s2
  • E 8 . 6 7 × 1 0 m/s2

How much velocity increase of the toy spacecraft would the sail produce in one day’s acceleration? Consider one day as 8 6 . 4 × 1 0 seconds.

Q7:

A 𝛾 -ray photon has a momentum of 8 . 0 0 × 1 0 kg⋅m/s.

Find the photon’s wavelength.

Find the photon’s energy.

Q8:

What is the energy of a photon whose momentum is 3 . 0 0 × 1 0 kg⋅m/s?

Q9:

A photon has a 1.00-Å wavelength.

Find the photon’s momentum.

  • A 5 . 7 8 × 1 0 kg⋅m/s
  • B 5 . 3 3 × 1 0 kg⋅m/s
  • C 6 . 1 4 × 1 0 kg⋅m/s
  • D 6 . 6 2 × 1 0 kg⋅m/s
  • E 7 . 0 3 × 1 0 kg⋅m/s

Find the photon’s energy.

Q10:

A 30.0-kV potential is used to accelerate the electrons in an old color television’s cathode-ray-tube. The electrons generate 𝑋 -rays when they strike the television’s screen. What is the shortest wavelength of these 𝑋 -rays?

  • A 2 . 8 4 × 1 0 m
  • B 5 . 9 1 × 1 0 m
  • C 5 . 1 0 × 1 0 m
  • D 3 . 6 7 × 1 0 m
  • E 4 . 1 3 × 1 0 m

Q11:

What is the minimum frequency of a photon required to ionize a H e + ion in its ground state if the energy required is 54.4 eV?

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

Q12:

An X-ray photon has an energy of 15 keV and a gamma ray photon has an energy of 3.2 MeV.

Find the wavelength of the X-ray photon.

Find the wavelength of the gamma ray photon.

  • A 1 . 0 × 1 0 nm
  • B 3 . 9 × 1 0 nm
  • C 4 . 1 × 1 0 nm
  • D 3 . 5 × 1 0 nm
  • E 2 . 9 × 1 0 nm

Q13:

X-rays are produced by striking a target with a beam of electrons. Prior to striking the target, the electrons are accelerated by an electric field through a potential energy difference of Δ 𝑈 = 𝑒 Δ 𝑉 , where 𝑒 is the charge of an electron and Δ 𝑉 is the potential difference. If Δ 𝑉 = 3 0 k V , what is the minimum wavelength of the emitted radiation?

Q14:

An X-ray tube accelerates an electron with an applied voltage of 50 kV toward a metal target, resulting in the generation of X-ray radiation.

What is the shortest-wavelength X-ray radiation generated at the target?

  • A 35 pm
  • B 25 pm
  • C 17 pm
  • D 42 pm
  • E 29 pm

Calculate the photon energy in electron volts of the shortest-wavelength X-ray radiation produced.

  • A 35 keV
  • B 43 keV
  • C 50 keV
  • D 73 keV
  • E 30 keV

Q15:

An X-ray tube has an applied voltage of 100 kV.

In kilo-electron volts, what is the most energetic X-ray photon that the tube can produce?

In joules, what is the most energetic X-ray photon that the tube can produce?

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

What is the wavelength of the most energetic X-ray photon that the tube can produce?

Q16:

An excimer laser used for vision correction emits photons with a wavelength of 185 nm. The photons are used to evaporate corneal tissue, which is very similar to water in its properties.

Calculate the photon energy in electron-volts.

Calculate the amount of energy needed per molecule of water to make the phase change from liquid to gas. Use a value of 2,257 kJ/kg for the heat of vaporization of the corneal tissue.

  • A 5 . 8 1 × 1 0 J
  • B 5 . 3 5 × 1 0 J
  • C 5 . 2 7 × 1 0 J
  • D 6 . 2 5 × 1 0 J
  • E 6 . 7 6 × 1 0 J

Find the ratio of the energy needed to vaporize a water molecule to the photon energy.

Q17:

Find the wavelength of a photon with a momentum of 3 . 6 5 × 1 0 kg⋅m/s.

  • A 5 . 8 4 × 1 0 m
  • B 1 . 1 4 × 1 0 m
  • C 1 . 8 2 × 1 0 m
  • D 2 . 8 9 × 1 0 m
  • E 6 . 6 1 × 1 0 m

Q18:

What is the momentum of a 600 nm photon?

  • A 9 . 0 6 × 1 0 kg⋅m/s
  • B 5 . 4 8 × 1 0 kg⋅m/s
  • C 4 . 0 2 × 1 0 kg⋅m/s
  • D 6 . 9 4 × 1 0 kg⋅m/s
  • E 1 . 1 0 × 1 0 kg⋅m/s

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