# 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 Hz
• B Hz
• C Hz
• D Hz
• E Hz

What is this photon’s wavelength?

• A m
• B m
• C m
• D m
• E m

Q2:

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

• A
• B
• C
• D
• E

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?

• A kg⋅m/s
• B kg⋅m/s
• C kg⋅m/s
• D kg⋅m/s
• E 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 kg⋅m/s
• B kg⋅m/s
• C kg⋅m/s
• D kg⋅m/s
• E kg⋅m/s

How much force is exerted on the mirror?

• A N
• B N
• C N
• D N
• E 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?

• A N/m2
• B N/m2
• C N/m2
• D N/m2
• E N/m2

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

• A m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

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

Q7:

A -ray photon has a momentum of kg⋅m/s.

Find the photon’s wavelength.

Find the photon’s energy.

Q8:

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

Q9:

A photon has a 1.00-Å wavelength.

Find the photon’s momentum.

• A kg⋅m/s
• B kg⋅m/s
• C kg⋅m/s
• D kg⋅m/s
• E 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 m
• B m
• C m
• D m
• E m

Q11:

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

• A Hz
• B Hz
• C Hz
• D Hz
• E 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 nm
• B nm
• C nm
• D nm
• E 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 , where is the charge of an electron and is the potential difference. If , 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?

• A J
• B J
• C J
• D J
• E 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 J
• B J
• C J
• D J
• E 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 kg⋅m/s.

• A m
• B m
• C m
• D m
• E m

Q18:

What is the momentum of a 600 nm photon?

• A kg⋅m/s
• B kg⋅m/s
• C kg⋅m/s
• D kg⋅m/s
• E kg⋅m/s