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?

  • A5.50×10 Hz
  • B4.98×10 Hz
  • C5.14×10 Hz
  • D5.33×10 Hz
  • E4.84×10 Hz

What is this photon’s wavelength?

  • A5.92×10 m
  • B7.21×10 m
  • C6.79×10 m
  • D6.20×10 m
  • E6.44×10 m

Q2:

An AM radio transmitter radiates 5.00×10 W of electromagnetic radiation at a frequency of 7.60×10 Hz. How many photons per second does the transmitter emit?

  • A8.46×10
  • B9.23×10
  • C9.61×10
  • D8.85×10
  • E9.93×10

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 mega-electron volts of a photon having a wavelength of 1.00 picometer.

Q4:

What is the momentum of a photon of wavelength 4.00 centimeters?

  • A1.41×10 kg⋅m/s
  • B1.53×10 kg⋅m/s
  • C1.17×10 kg⋅m/s
  • D1.28×10 kg⋅m/s
  • E1.66×10 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?

  • A1.71×10 kg⋅m/s
  • B0.707×10 kg⋅m/s
  • C1.59×10 kg⋅m/s
  • D1.33×10 kg⋅m/s
  • E1.01×10 kg⋅m/s

How much force is exerted on the mirror?

  • A2.26×10 N
  • B1.01×10 N
  • C1.33×10 N
  • D1.82×10 N
  • E2.68×10 N

Q6:

Radiation known as the solar wind is incident on the top of Earth’s atmosphere 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 that 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?

  • A8.28×10 N/m2
  • B8.43×10 N/m2
  • C8.67×10 N/m2
  • D9.19×10 N/m2
  • E8.90×10 N/m2

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

  • A9.03×10 m/s2
  • B8.67×10 m/s2
  • C6.63×10 m/s2
  • D8.05×10 m/s2
  • E7.36×10 m/s2

How much velocity increase of the toy spaceship would the sail produce in one day’s acceleration? Consider one day as 86.4×10 seconds.

Q7:

A 𝛾-ray photon has a momentum of 8.00×10 kg⋅m/s.

Find the photon’s wavelength.

Find the photon’s energy.

Q8:

What is the energy of a photon whose momentum is 3.00×10 kg⋅m/s?

Q9:

A photon has a 1.00-Å wavelength.

Find the photon’s momentum.

  • A7.03×10 kg⋅m/s
  • B6.62×10 kg⋅m/s
  • C5.33×10 kg⋅m/s
  • D6.14×10 kg⋅m/s
  • E5.78×10 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?

  • A4.13×10 m
  • B5.10×10 m
  • C2.84×10 m
  • D3.67×10 m
  • E5.91×10 m

Q11:

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

  • A1.42×10 Hz
  • B1.31×10 Hz
  • C1.50×10 Hz
  • D1.24×10 Hz
  • E1.15×10 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.

  • A3.9×10 nm
  • B2.9×10 nm
  • C4.1×10 nm
  • D3.5×10 nm
  • E1.0×10 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 Δ𝑈=𝑒Δ𝑉, where 𝑒 is the charge of an electron and Δ𝑉 is the potential difference. If Δ𝑉=30kV, 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?

  • A35 pm
  • B42 pm
  • C25 pm
  • D29 pm
  • E17 pm

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

  • A30 keV
  • B50 keV
  • C35 keV
  • D43 keV
  • E73 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?

  • A1.38×10 J
  • B1.68×10 J
  • C1.56×10 J
  • D1.48×10 J
  • E1.60×10 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.

  • A5.27×10 J
  • B5.81×10 J
  • C6.76×10 J
  • D5.35×10 J
  • E6.25×10 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 3.65×10 kg⋅m/s.

  • A1.14×10 m
  • B2.89×10 m
  • C1.82×10 m
  • D6.61×10 m
  • E5.84×10 m

Q18:

What is the momentum of a 600 nm photon?

  • A4.02×10 kg⋅m/s
  • B5.48×10 kg⋅m/s
  • C1.10×10 kg⋅m/s
  • D9.06×10 kg⋅m/s
  • E6.94×10 kg⋅m/s

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