Homework on the Photoelectric Effect, 2000 version (solutions)

Feel free to work on the homework in groups. The work you hand in, however, should reflect your understanding of the material. You should show all of your calculations (neatly) and justify all of your answers for full credit.

Light of wavelength 525 nm shines on a piece of metal, causing electrons to be emitted from the metal.

1. What is the frequency of the light?
Light travels at velocity c = 3 x 10⁸ m/s. Making use of the expression, c = fl, f = c/l = 3 x 10⁸ / 525 x 10^-9m = 5.7 x 10¹⁴ s^-1

2. What is the energy of a single photon in the light in Joules? E = hf = hc/l = 1240 eV nm / 525 nm = 2.36 eV = 3.77 x 10^-19 J

3. Removing an electron from the metal requires 1.2 eV. How many Joules is that?
The conversion between eV and J is: 1 eV = 1.6 x 10^-19 J 1.2 eV * 1.6 x 10^-19 = 1.9 x 10^-19 J

4. What will be the kinetic energy of electrons ejected from this metal by the light in Joules?
Each electron is given the total energy of the photon it interacts with. To get out of the metal it gives up some of this energy to overcome the potential energy of the work function. The rest of the energy is seen as kinetic if it is not lost to collisions. K_e- = E_photon – work function = 1.87 x 10^-19 J

5. The intensity of the light is doubled. What happens to the kinetic energy of the electrons? What happens to the rate at which electrons are emitted by the metal?
Doubling the intensity of light means that the number of particles impinging on a given in area in a given time will double. Since photons interact with on electron only, this means a doubling in the number of electrons ejected in a given time will occur but the kinetic energy of the ejected electrons will be unchanged.

6. The wavelength of the light is halved. What happens to the kinetic energy of the electrons? What happens to the rate at which electrons are emitted by the metal? (Be careful: halving the wavelength results in doubling the frequency).
Halving the wavelength doubles the frequency and, thus, doubles the energy of the incident photons. This doubles the energy given to each electron, nearly doubling its kinetic energy after it is free from the metal. However, the number of electrons ejected in given time will remain constant due to the one photon/ one electron interaction.

7. What quantum paradox bothers you the most? Explain how it results from quantum theory and why it seems contradictory to common sense.

1.	What is the frequency of the light? Light travels at velocity c = 3 x 10⁸ m/s. Making use of the expression, c = fl, f = c/l = 3 x 10⁸ / 525 x 10^-9m = 5.7 x 10¹⁴ s^-1
2.	What is the energy of a single photon in the light in Joules? E = hf = hc/l = 1240 eV nm / 525 nm = 2.36 eV = 3.77 x 10^-19 J
3.	Removing an electron from the metal requires 1.2 eV. How many Joules is that? The conversion between eV and J is: 1 eV = 1.6 x 10^-19 J 1.2 eV 1.6 x 10^-19 = 1.9 x 10^-19 J*
4.	What will be the kinetic energy of electrons ejected from this metal by the light in Joules? Each electron is given the total energy of the photon it interacts with. To get out of the metal it gives up some of this energy to overcome the potential energy of the work function. The rest of the energy is seen as kinetic if it is not lost to collisions. K_e- = E_photon – work function = 1.87 x 10^-19 J
5.	The intensity of the light is doubled. What happens to the kinetic energy of the electrons? What happens to the rate at which electrons are emitted by the metal? Doubling the intensity of light means that the number of particles impinging on a given in area in a given time will double. Since photons interact with on electron only, this means a doubling in the number of electrons ejected in a given time will occur but the kinetic energy of the ejected electrons will be unchanged.
6.	The wavelength of the light is halved. What happens to the kinetic energy of the electrons? What happens to the rate at which electrons are emitted by the metal? (Be careful: halving the wavelength results in doubling the frequency). Halving the wavelength doubles the frequency and, thus, doubles the energy of the incident photons. This doubles the energy given to each electron, nearly doubling its kinetic energy after it is free from the metal. However, the number of electrons ejected in given time will remain constant due to the one photon/ one electron interaction.
7.	What quantum paradox bothers you the most? Explain how it results from quantum theory and why it seems contradictory to common sense.