For this experiment, please go to this website: https://phet.colorado.edu/sims/p

Question

For this experiment, please go to this website:

https://phet.colorado.edu/sims/photoelectric/photoelectric_en.jnlp

Please make sure that you have installed the latest version of Java to run this application.

Objective

In this experiment, the aim is to measure and confirm the work function of a known metal and to determine Planck constant. The experiment is then repeated for an unknown metal to determine its work function.

Theory

In applying the Einstein’s photoelectric effect model, we derive the following expression:

Kmax = hf – W                                                                                      (1)

where Kmax is the kinetic energy of the most energetic emitted electrons, h is the Planck constant, f is the frequency of the light, and W is the work function of the metal.

In this experiment, you set the values of f, while determining the corresponding stopping potential Vstop. Vstop is defined as the potential between the cathode and the anode that just barely stop the most energetic electron from reaching the anode. Once Vstop has been found, you will have obtained the value of Kmax.

Part A

{Note: In using the Photoelectric effect applet, do not pay too much attention to the animation (i.e. the emitted electrons). Pay attention only to the reading on the current and the setting of voltage on the anode. If the current reads “zero” even when you see an animation of electrons being emitted, take that to be zero current.}

You will be measuring the stopping potential Vstop for various wavelength l of light frequencies. Using these values, you will determine the work function and the threshold frequency from your graph.

Set your Applet to the following parameters:

            Target: Sodium

            Intensity: 100%

            Light Source Wavelength: 540 nm

            Battery Voltage: 0.00 V

Run the applet. At these settings, you should see no electron emission, and the current should read zero.

Change the wavelength setting slowly to lower values until you notice the first non-zero current (ignore the animation).

Slowly and carefully change the battery voltage until you get the first voltage where the current goes to zero. This is Vstop for this wavelength of light. (Hint 1: you want a negative voltage. Hint 2: it might be easier to click on the box containing the value of the voltage, and manually change the numbers, rather than using the slider). Please note that you want the smallest magnitude of the negative voltage where the current first goes to zero. So try and determine this as accurately as possible.

     

Record the wavelength l and the stopping voltage Vstop in the table below. Repeat for several other wavelengths and record your data in the table. To find f, use c = fl. To find Kmax, use Kmax = eVstop. (5 points)

l (nm)

f (Hz)

Vstop (V)

Kmax (eV)

Using Eq. 1, explain how, using your data and a proper graph, you will be able to determine the value of Planck constant h and the work function W of sodium. (3 points)

Plot a graph of Kmax versus f. Show clearly the proper curve fit and fitting parameters. (3 points)

Using your fitting parameters, determine the Planck constant and the work function of sodium. (3 points)

Compare your results with the accepted values. What are the percentage differences? (The book value for h = 4.135×10-15 eVsec, and W for sodium is 2.28 eV.) (2 points)

From your graph, what is the threshold frequency? (1 point)

The threshold frequency occurs at Kmax = 0. From Eq. 1, this means that hfthreshold = W. Use the value of your threshold frequency to find another experimental value of the work function of sodium. How different is this value from the one you obtained in #7? (3 points)

Part B

Repeat the parameter settings in #1 of Part A, but this time, replace sodium with the unknown metal ?????

As in #2, slowly change the wavelength of light until you see the first non-zero current. (i) Is this wavelength where you first see a non-zero current longer or shorter than the one for sodium? (ii) From this observation alone, do you expect the work function of this unknown metal to be higher or lower than sodium? Explain. (2 points)

Repeat the experiment from Part A. Fill the data table and plot your graph. (4 points)

From your data and graph, determine the work function of this unknown metal. You only need to determine the work function via just one technique. You do not need to re-determine the Planck constant. (2 points)

Is the value of the work function of this unknown metal matches your expectation in #11? Explain (2 points)

  

l (nm)

f (Hz)

Vstop (V)

Kmax (eV)

Explanation / Answer

Part A)   work function = 0.574 eV

=>   Vstop =   4.53 mV

=> threshold frequency = 1.33 * 106 Hz

=> percentage differences = 0.543 %

Part B)   the work function of this unknown metal is higher than sodium .

=>    the work function of this unknown metal =    0.623 eV

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