We can predict the positions of the maxima and minima in the diffraction and interference patters produced by single and multiple slits by assuming that light is an EM wave. Where crests meet crests and troughs meet troughs we predict and observes maxima or bright regions, and where crests meet troughs we predict and observe minima or dark regions.

In this assignment you will simulate an experiment that suggests that light is a particle. You will investigate the photoelectric effect. To demonstrate this effect, light is shone on a metal surface and ejected electrons are detected. To eject an electron from a metal surface a certain amount of energy Φ must be supplied to this electron. Φ is called the work function of the metal. (If no energy were required to free the electrons, they would just leave ordinary pieces of metal.) In the wave picture the energy of the light beam does not depend on the frequency, but only on the intensity, which is proportional to the square of the amplitude.

If the frequency of the light is higher than the **cutoff frequency**
f_{c}, then electrons are released. No
electrons are emitted if the frequency of the light falls below
this cutoff frequency f_{c}. For many
metal surfaces the frequency of blue light is greater than f_{c} and the
frequency of red light is less than f_{c}. If
red light is shone on the surface, no electrons are emitted, no matter what the
intensity of the light (within reasonable limits). If blue light is shone
on the surface, electrons are emitted. The number of emitted electrons
depends on the intensity of the light. But even if the intensity is reduced to a very
low value, electrons are still emitted, albeit at a very low rate.
These observations constitute **the photoelectric effect**.

Einstein explained the photoelectric effect by assuming that the energy and momentum transported by an
electromagnetic wave are not continuously distributed over the wave front.
They are transported in discrete packages. **Photons** are the particles of light. Light is "quantized".
Photons always move with the speed of light. The energy of each photon is
E = hf = hc/λ. The momentum of each photon is E/c = hf/c = h/λ.

h = 6.626*10^{-34}J s = 4.136*10^{-15} eV s = Planck's constant.

unit of energy: 1 eV = 1.6*10^{-19} J.

useful product: hc = 1240 eV nm.

An electron can only receive the large amount of energy necessary to escape the metal from the EM wave by absorbing a single photon. If this photon has enough energy, the electron is freed. Excess energy appears as kinetic energy of the electron. The maximum kinetic energy of the electron is given by E = hf - Φ. If the photon does not have enough energy, then the electron cannot escape the metal.

You will direct light with different wavelength onto a metal surface and measure the kinetic energy of the photoelectrons ejected from the metal as a function of the frequency of the light used to eject the electrons. You will measure the work function of the metal and also determine the value of Planck's constant h from your data. This experiment reveals the "particle nature" of light.

Open a Microsoft Word document to keep a log of your experimental procedures,
results and discussions.

Address the points highlighted in blue. Answer all questions.

You will use an on-line simulation from the University of Colorado PhET group.

Link to the simulation:
http://phet.colorado.edu/en/simulation/photoelectric

Explore the interface. There are some non-obvious controls.

- You can select Show photons in the Options menu to show the light beam as composed of individual photons.
- You can select Control photon number instead of intensity in the Options menu to change the Intensity slider to a Number of photons slider.
- You can use the camera icon to take a snapshot of the graphs so that you can compare graphs for different settings.
- You can Pause the simulation and then use Step to incrementally analyze.

In the simulation photons strike a metal cathode and eject electrons. Electrons are ejected with a range of energies, up to a maximum energy. The electrons are collected on the anode and then flow back from the anode to the cathode through a wire. The current in the wire is measured. Electrons are negatively charged. If the anode is at a positive voltage compared to the cathode, electrons are attracted and gain energy. If the anode is at a negative voltage compared to the cathode, electrons are repelled and loose energy.

Let V_{ca} = V_{cathode} - V_{anode}. If this potential difference V_{ca} (energy per charge) becomes large
enough, electrons will no longer reach the anode and current will no longer flow in the wire.

It is convenient to measure electron energy in units of electron volt (eV). In SI units 1 eV = 1.6*10^{-19 }J.

If the potential difference between the cathode and anode is x volts (V_{ca} = x V), then electrons ejected from the
cathode need an energy of at least x eV to overcome this potential difference
and to reach the anode. By determining voltage V_{ca} needed to reduce the
current in the wire to zero, we can determine the maximum energy
of the ejected electrons. The maximum energy E of electrons that reach the anode in eV has the same
numerical value as the voltage in V_{ca}.

(a) Exploration:

For a Sodium target discuss:

- For a fixed number of photons and zero battery voltage, how does the number of photoelectrons ejected depend on the wavelength? Does every photon eject an electron? Does the probability of ejection change with wavelength? Discuss!
- For a fixed wavelength and zero battery voltage, how does the current depend on the light intensity? Discuss!
- For a fixed wavelength and light intensity, how does the current depend on the battery voltage?
- For a fixed wavelength and light intensity, do all ejected electrons have the same energy? How can you measure the maximum energy of the ejected electrons.

(b) Measurement:

Use a Sodium target. Set the
intensity to 100%. For the wavelengths listed in the table below, find the
maximum energy of the ejected electrons by finding the battery voltage V_{ca}
that just prevents the most energetic electrons from reaching the anode.

Note: The text box under the battery displays -V_{ca}.

Wavelength (nm) | Frequency (s) | Maximum Electron Energy (eV) |
---|---|---|

150 | 2.00e15 | |

200 | 1.50e15 | |

300 | 1.00e15 | |

400 | 0.75e15 | |

500 | 0.60e15 |

Prepare a graph of the maximum electron energy versus
the frequency of the light. Choose a X-Y Scatter plot. Plot maximum electron energy on the vertical axis and frequency on the
horizontal axis.

Prediction: E = hf - Φ

This equation is of the form y = ax + b, with a being the slope and b being the
y-intercept. The slope of the plot of E versus f will yield Planck's constant
and the y-intercept will yield the work function of the metal cathode.

Add a trendline and insert the equation for the trendline into your plot. Use
the slope of your trendline to find Planck's constant h and the intercept value
to find the work function Φ of Sodium. If
there are data points that seem to deviate to far from the trendline, repeat
those measurements until you are satisfied that you have done your best.

Since the electron energy is measured in eV and the
frequency in seconds, Planck's constant h will have units of eV s and the work
function will have units of eV. Convert Planck's constant to SI units (J s) by
multiplying the value you obtained from the slope by 1.6*10^{-19}J/eV.

Insert your table into your Word document.

- What value did you obtain for h in units of eV s and J s?
- How does this value compare with the accepted value
h = 6.626*10
^{−34}J s = 4.136*10^{−15}eV s? - Describe how the maximum energy of the photoelectrons depends on the wavelength of the incident light.
- Defend whether this experiment supports a wave or a quantum model of light based on your lab results.

To earn extra credit add your name and e-mail address to your Word document. Save your Word document (your name_exm9.docx), go to Canvas, Assignments, Extra Credit 9, and submit your document.