# Planck's Constant

Lab Partner: Boleszek Notes and data taken during the lab are contained within his lab notes/report HERE

The basic lab procedures were taken from chapter 5 of professor Gold's manual: [lab manual]

## Purpose

To calculate the value of Plank’s constant by measuring the energy in different frequencies of light.

## Procedure

Plank’s great discovery that we are investigating here is that the energy in a photon is directly proportional to it’s frequency. Assuming this to be true, then via the photoelectric effect, an electron freed from a substance will have the energy of that photon minus the work function for that substance (energy required to free the electron).

The energy in a photon can be measured directly by measuring the strength of an electric field required to stop it from moving (stopping potential). In this lab the stopping potential and the photoelectric effect were provided by a photodiode connected to a high impedance 1:1 amplifier. This simple circuit works fairly well, but the user needs to be aware that it is a real circuit and therefore has some small current leakage. Also the circuit is sensitive enough to be susceptible to small capacitive changes, such as those produced by simply touching the apparatus.

As suggested by the lab manual, we acquired two separate sets of data. The first was to observe the time that it takes to reach a given potential with different intensities of light. Allowing for some small current leakage, it can be observed that the voltage produced by a given color was dependent only upon it’s frequency, and the intensity of the light was responsible only for the current. The interpretation of this fact is that the energy in the photon freed the electron has a certain amount of energy directly related to the frequency of the light incident on the device. This is a strong piece of evidence in favor of light packages having frequency dependent energy. More photons freed in this experiment will mean more electrons flowing (i.e. higher current, which is indicated by a faster charge of the capacitance of the photodiode). But the energy of any light charge has a maximum value not exceeded and always reached.

The second portion of this experiment was to actually measure the stopping voltage from several frequencies and use this to calculate Plank’s constant. For the most part this is easily done. However, there was a problem with the 2nd order green spectrum. It was observed that with these tools the green spectrum in the second order produced a voltage that was far out of expected range, disagreeing with the expected linear nature of the experiment and the values in the first order data. We checked this value by measuring the stopping voltage produced by the dark bands on either side of the green band and found very similar values to that produced by the green band. This lead us to believe that the measurement of the green was being swamped by a small amount of non-visible spectrum light being spread by the lens. To check this we used a clear UV filter (In the form of my eye glasses) and reacquired green spectrum data. This was much closer to the expected value and we used these for our second order green data. SJK 17:53, 2 November 2008 (EST)

17:53, 2 November 2008 (EST)
I thought it was really cool how you investigated the "dark" bands and thus got a really great insight into the green band problem. Very cool that your UV-blocking lenses did the trick.

## Calculations

Planks constant was calculated by plotting light frequency vs. electron energy. The data was processed by averaging the data points by freq and then using the Matlab fit function for a first order polynomial.

By Plank’s equation h = KE/freq +Work/freq

Therefore, the slope of the line produced by the fit is Plank’s constant and the y intercept is the negative of the work function. From our data and calculations the results of this experiment were

Plank’s constant = 7.184 × 10-34 +/- 0.33 × 10-34 m2 kg / s (Steve Koch:This would be more easily read and interpreted written as (7.18 ± 0.33) x 10-34 J-s or 7.18(33) x 10-34 J-s)

This is within 9% of the accepted value of 6.626068 × 10-34 m2 kg / s.

There were few data points taken and they were fairly well repeated, which may indicate that errors produced were systematic, but we would require further investigation to isolate these.

Errors based on data acquisition variability were examined by taking the standard deviation of each data point and adding this back into the averaged data to calculate the effects on the final outcome.SJK 18:14, 2 November 2008 (EST)

18:14, 2 November 2008 (EST)
After about 15 minutes of looking at your code and this paragraph, I still can't figure out what you did to get these two error values. What you need is a primary notebook page (in addition to the one shared with Boleszek) where you describe your methods more thoroughly, and show all the outputs of your matlab code (graphs with fits, etc.). It does look like you generated graphs with your code...I want to see them!

By this method, error attributed to data acquisition inconsistencies are only +/-1.2E-036.SJK 18:32, 2 November 2008 (EST)

18:32, 2 November 2008 (EST)
OK, I think I understand the first method now. I don't think it's a method you can expect to work. If the standard deviation of all data points were constant, then the effect on the slope would be zero. In fact, as I'll show on Monday, linear regression has accepted ways of producing an uncertainty in the slope. Also, you could look at the SEM of the mean planck's constant for all four data sets. I don't know where you get the 0.33E-34 error.

However, because so few data points were acquired, the confidence level of the curve fit is +/- 0.33E-34. This is adopted here as the dominant source of error. However, considering the repeatability of the few data points acquired, it seems likely that an as yet undiscovered systematic error(s) exist which could perhaps be revealed with more careful acquisition.

All calculations and analysis were carried out entirely within this Matlab file: [1]