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

So light is a wave, these experiments settle this?  Not so fast!

In this laboratory you will perform an experiment that suggests that light is a particle.  You will investigate the photoelectric effect.  To eject an electron from a metal surface a certain amount of energy Φ, called the work function of the metal, must be supplied to this electron.  (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.  Einstein explained the photoelectric effect by postulating that 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.

In this laboratory you will direct yellow, green, blue, violet and ultraviolet light 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 from your data.

#### Equipment needed:

• mercury light source
• diffraction grating with focusing lens on a mounting bracket
• photoelectric head with built-in instrument amplifier
• set of yellow and green filters
• digital voltmeter

Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions. This log will become of your lab report.  Address the points highlighted in blue.  Answer all questions.

Exploration:

Before stating the experiment, work with an on-line simulation from the University of Colorado PhET group.

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

• You can elect 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.

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.

Now try the other targets.  What is the longest wavelength (λmax) light can eject electrons from those targets?  What is the work function Φ = hc/λmax of these targets?  Complete the table and paste it into your log.

(Remember: hc = 1240 eV nm)

 Target λmax for electron ejection (nm) Φ = hc/λmax (eV) Sodium Zinc Copper Platinum Calcium ?????

Experiment:

The apparatus is shown on the right.

The light source is a mercury vapor lamp. The mercury atoms produce strong emission lines at different frequencies or colors.

 Color Wavelength (nm) Frequency (1014/s) Yellow 578&580 5.19 Green 546.1 5.48 Blue 435.8 6.88 Violet 404.7 7.41 Ultraviolet 365.5 8.20

Photons of light of different colors are separated by a transmission grating that diffracts light of different colors into different directions.  A lens focuses the light onto a photoelectric head, where the photons strike a metal cathode and eject electrons.  The electrons are collected on the anode.

In the simulation you just explored, the electrons flow back from the anode to the cathode through a wire, and the current in the wire is measured. In our experiment we do not connect the cathode and anode with a wire, but with a voltmeter.  No current flows through an ideal voltmeter.  The electrons cannot leave the anode.

Electrons are negatively charged, and as more and more electrons gather on the anode, the anode becomes more and more negatively charged.  A potential difference or voltage develops between the cathode and the anode.  The electrons already collected on the anode repel electrons ejected from the cathode at a later time.  It is convenient to measure the electron energy in units of electron volt (eV). In SI units 1 eV = 1.6*10-19J.  If the potential difference between the cathode and anode has grown to x volts, 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 measuring the maximum voltage between cathode and anode, we can determine the maximum energy of the electrons that reached the anode.

The maximum energy E of electrons that reached the anode in eV has the same numerical value as the maximum voltage in V.

Schematic of the photoelectric head showing the cathode and anode.

(a) Set up the apparatus as shown in the figure above.  The light source should have a slit assembly mounted in place with a lens/grating assembly attached by two rods.  The grating should be mounted away from the light source and should not be touched with fingers in making any adjustments.  Take a look at the apparatus and identify the following pieces:
• Mercury lamp; you should switch this on now (if it is not already on) so that it can start warming up.
• The light exits the mercury lamp through a small rectangular aperture of size 2.4 mm x 27 mm to make a well-defined beam.
• The next object in the optical path is a combined lens and diffraction grating.  The lens is a 100 mm focal length lens that focuses the light onto the vacuum photodiode inside the photoelectric effect apparatus.  It is followed by a diffraction grating (600 lines/mm).  This grating is blazed meaning it produces the brightest spectrum on one side only.
• The light then travels to the photoelectric head.  It first encounters a rectangle with a white reflective mask; this mask allows you to see the ultraviolet line from the mercury source that is not normally visible.  It is made of a special fluorescent material that makes the ultraviolet line appear as a blue line, and it also makes the violet line appear more blue.  Light passes through this aperture into a light shield that you can flip out of the way (try it).  This light shield should always be closed when you do measurements so that room light doesn’t get into the device.
• The photoelectric head also has voltage outputs, and it should be connected up to a handheld digital voltmeter.
• The vacuum photodiode that you will use in this experiment is contained in a shielded enclosure inside the photoelectric head, so you won’t be able to see its details.  A schematic is shown above.

(b) Your mercury lamp should have been on at least 10 minutes to warm up.  Rotate the photoelectric effect head on its swinging coupling bar so that the zeroth order of the diffraction grating strikes the white reflective mask on the front of the photoelectric head.  If the light image doesn’t appear well focused, you can adjust the position of the lens/grating assembly; adjust it by loosening the thumbscrew and sliding it along its rods.

(c) Roll the light shield out of the way to reveal the white photodiode mask inside the apparatus.  You now need to rotate the photoelectric head on its support rod until the input light is passing through the input rectangular aperture and is striking the holes in front of the photodiode.  Once you have it adjusted properly, tighten the thumbscrew in the base support rod.  Unfortunately, even when this thumbscrew is tight the apparatus can still rotate a little bit, so you have to be careful not to bump it.  You may also need to adjust the lens/grating assembly a bit to achieve the sharpest possible image of the aperture on the window in the photodiode mask. Then roll the light shield back into place.  Whenever you move to a different wavelength of light, you need to open the light shield and recheck that the light is striking the phototube inside the apparatus.

(d) Turn the power switch of the photoelectric head ON.  Now rotate the entire photoelectric head about the pin in the coupler bar until you see the colored maxima in first order.  Swing to either side of the zeroth order and figure out which side the first order maxima appears to be brighter on (it will be brighter on one side since this is a blazed diffraction grating).  Make sure that you can identify all five spectral lines listed in the table below.

(e) Pick out one of the lines in first order (on the bright side) and make sure it is striking the photodiode following the procedure in step (c).  For the green and yellow lines you need to use the filters provided to limit other frequencies of light from entering the apparatus.  Place the appropriate filter (green or yellow) on the white reflective mask.  Press the “PUSH TO Zero” button on the side of the photoelectric head.  This will discharge any charge built up on the anode.  Release the button, and then look at the voltage on the voltmeter.  You will see it immediately jump up to some non-zero value and then, depending on the light intensity, it may take a few (sometime as long as 30 – 40 seconds) to settle at its final value.  The final, stable voltage value on the voltmeter is the stopping potential for that wavelength of light.  Open Excel and prepare a table as shown to the right.  Enter your measured maximum electron energy in eV for your chosen color into the table.

 Color Frequency (/s) Maximum Electron Energy (eV) Yellow 5.19e14 Green 5.48e14 Blue 6.88e14 Violet 7.41e14 Ultraviolet 8.20e14

Adjust the apparatus and position the head to measure the stopping voltage for each of the five colors listed in the table and enter the maximum electron energy into the table.

(f) 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 the photocathode material of the phototube.  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.

(e) 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*10-19J/eV.

(g) Repeat all your measurements with dimmer lines from the second order pattern or from the first order pattern on the opposite side.  Measure the maximum electron energy for these lines and compare with the values you previously obtained using the first-order, bright pattern.

Turn the power switch of the photoelectric head OFF.

Insert your tables obtained using the bright lines and the dimmer lines, respectively, into your log and comment on your results.

• 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 the effect that different colors of light had on the stopping potential and thus the maximum energy of the photoelectrons.

• Describe the effect that the different light intensity had on the stopping potential and thus the maximum energy of the photoelectrons.  Do you see an effect?  Did you expect an effect?  Think about your measuring instrument. (No current flows through an ideal voltmeter.  But a real digital voltmeter measures voltage by drawing a small amount of current.  What can happen if the light intensity is low and few photoelectrons are ejected?)

• Defend whether this experiment supports a wave or a quantum model of light based on your lab results.

Open Microsoft Word and prepare a report.