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