Physics307L:People/Phillips/Photoelectric

Photoelectric Effect (Planck's Constant) Summary

Data & Results

The notebook entry for this lab is located here. We generated two Excel files for this lab as well: Planck.xlsx and First Order.xlsx.

In this lab, we showed by experiment that the energy stored in light is proportional to it's frequency (not amplitude) and determined what this constant of proportionality is, as well as another constant that shows up from photoelectric effect theory.

We measured two different things in this lab related to the photoelectric effect, but only one of these has an accepted value - Planck's Constant. This value is

[math]\displaystyle{ h_{acc} = 6.626\,068\,96(33) \times 10^{-34}~\mathrm{J}\cdot\mathrm{s} = 4.135\,667\,33(10) \times 10^{-15}~\mathrm{eV}\cdot\mathrm{s} }[/math]

We came up with many different value for Planck's constant. We obtained two from the first order maxima from the light source, each being a separate run through the colors:

[math]\displaystyle{ h^{1}_{first order} = (6.911 \pm .087) \times 10^{-34}~\mathrm{J}\cdot\mathrm{s} = (4.319 \pm .054) \times 10^{-15}~\mathrm{eV}\cdot\mathrm{s} }[/math]

[math]\displaystyle{ h^{2}_{first order} = (6.978 \pm .059) \times 10^{-34}~\mathrm{J}\cdot\mathrm{s} = (4.361 \pm .037) \times 10^{-15}~\mathrm{eV}\cdot\mathrm{s} }[/math]

each with percent errors from the accepted value of

[math]\displaystyle{ \% error^{1}_{first order} = 4.30\% }[/math]

[math]\displaystyle{ \% error^{2}_{first order} = 5.32\% }[/math]

Along with these first order values, we also ran through the experiment using only the second order maxima, obtaining different values for Planck's constant:

[math]\displaystyle{ h^{1}_{second order} = (5.74 \pm .51)\times 10^{-34}~\mathrm{J}\cdot\mathrm{s} = (3.59 \pm .32) \times 10^{-15}~\mathrm{eV}\cdot\mathrm{s} }[/math]

[math]\displaystyle{ h^{2}_{second order} = (5.65 \pm .52)\times 10^{-34}~\mathrm{J}\cdot\mathrm{s} = (3.53 \pm .32) \times 10^{-15}~\mathrm{eV}\cdot\mathrm{s} }[/math]

again with respective percent errors from the accepted value

[math]\displaystyle{ \% error^{1}_{second order} = 13.4\% }[/math]

[math]\displaystyle{ \% error^{2}_{second order} = 14.8\% }[/math]

All of the above numbers enumerate our results for Planck's constant, but we also measure what the work function must be for the cathode that the light is incident upon. We obtained four total values for this as well, from the four runs mentioned above, but there is no accepted value to compare it with.

[math]\displaystyle{ W^{1}_{0} = (2.43 \pm .06) \times 10^{-19}~\mathrm{J} = (1.52 \pm .04)~\mathrm{eV} }[/math]

[math]\displaystyle{ W^{2}_{0} = (2.47 \pm .04) \times 10^{-19}~\mathrm{J} = (1.54 \pm .03)~\mathrm{eV} }[/math]

[math]\displaystyle{ W^{3}_{0} = (1.47 \pm .35) \times 10^{-19}~\mathrm{J} = (0.922 \pm .22)~\mathrm{eV} }[/math]

[math]\displaystyle{ W^{4}_{0} = (1.41 \pm .35) \times 10^{-19}~\mathrm{J} = (0.884 \pm .22)~\mathrm{eV} }[/math]

Notice how the work function results for the second order maxima (indexes 3 and 4) were significantly different from the first order results, but the errors were much larger.

Conclusions

This lab was very straightforward and easy to perform, but the results seem somewhat questionable. I think it's kind of strange how we were able to obtain quite good (as in close to accepted) results for the first order maxima but quite poor results for the second order maxima. This makes me wonder if we should have just thrown out the second order data set not just for Planck's constant but also for the work function. The only cause I could think of that might produce inaccurate results for these second order maxima is that perhaps the colors (i.e. frequencies) of incident light are interacting with each other in some way so we don't really get a single incident color. It also seems curious that we used light filters only for the yellow and green frequencies. Why didn't we use filters for every color in the Mercury spectrum?

Although this all seems strange and sketchy, we did end up with good results, at least for the first order set of data. One standard deviation used in the standard error of the mean did not get our values to lie very near the accepted value, but they were still pretty close. As for the work function, we can see that it takes approximately one electron-volt to knock an electron out of the cathode material that was incorporated into our photoelectric effect apparatus.