# Planck's Constant

Lab Partner: Alexander Barron

My Lab Notebook: Planck Lab Notes

## Experiment 1

Before we begin finding the particular relationships between photo-electron kinetic energy and the frequency, we need to validate whether the photo-electron kineitc energy depends entirely on frequency in the first place. This experiment is the basis of quantum physics, and was used to prove Einstein's Quantum Theory of light. We will prove that the kinetic energy is entirely dependent on the incident frequency of light, rather than the intensity of light as the classical wave model predicted.

Trial 1

Vstop vs. Transmission Charge Time vs. Transmission

Trial 2

Vstop vs. Transmission Charge Time vs. Transmission

Question 1: Describe the effect of the varying intensity on the stopping potential.

• As one can see from my plots the stopping potential varies on the order of a a few thousands of a Volt as we vary the intensity via the transmission filter. During the experiemtn we noticed that the voltage fluctuates at this same range for no apparent reason (maybe moving my hands around, or breathing) and so we can conclude that these variations in the potential are meaningless. That of course means that the stopping potential, and therefore the kinetic energy of the photo electrons is not dependent on the intensity of light.

Question 2: Describe the effect that different colors of light had on the stopping potential.

• The shorter wavelength light produces higher stopping potentials. This validates the fact that higher energy frequencies (shorter wavelength) have more energy to give to the photoelectrons, thus the photoelectrons receive more energy from higher frequencies and are able to leave the metal with a higher kinetic energy.

Question 3: Does this support wave thoeory of light or quantum?

• The old wave theory of light predicted that the kinetic energy of the photons would depend on the intensity of the incident light. Since we have shown this is not the case we have proven the wave theory of light invalid. The quantum theory of light, based on this experiment, is the new doctrine...that the kinetic energy of photo-electrons depend on the incident frequency, not intensity. We can show that this is most certainly the case by simply looking at teh stopping potentials of each color...

Color Max Voltage Trial 1 Max Voltage Trial 2
Yellow 0.714 V 0.711 V
Green 0.849 V 0.830 V
Blue 1.488 V 1.499 V
Violet 1.710 V 1.710 V
Ultraviolet 2.053 V 2.030 V

A trend can be seen that the higher the frequency (highest is ultraviolet at 8.20E14 Hz) of incident light, the higher the kinetic energy of the photoelectrons as indicated by the stopping potential.

Question 4: Explain why there is a slight drop in the measured stopping potential as the light intensity is decreased.

• My Yellow line plot is the best example of this, where the stopping potential does indeed drop beginningat about 20% intensity transmission. The lab manual says this is due to the high impedence amplifier that lets us measure the stopping potential right from the anode of the plate using a voltmeter. Charge leaks off, meaning that if it takes longer for the capacitor to charge up, it will leak more...kind of like a bath tub that drains. If you fill it up at a higher rate the leaking is neglible. But if you fill it up slow, the draining makes a bid difference. At low intensity light, the capacitor takes a while to charge up and thus the current drain is noticed.

### Conclusion of Experiment 1

We have validated the photon theory of light and can now proceed to determine the exact relationship between the frequency of incident light and the Kinetic Energy of these photo-electrons being emitted. We will use Einstein's Quantum Theory of the Photo-Electric Effect in the next part to determine the constant of relation.

## Experiment 2: Planck's Constant

Einstein's nobel prize relationship between incident frequency of light and the kinetic energy of the emitted photons is...

$\displaystyle hf=W_{o}+KE$

where we set out to determine the constant h by altering the equation to put it into a form that allows us to use the method of linear least squares...

$\displaystyle Vo=\frac{h}{e}f - \frac{W_{o}}{e}$

Plots with linear least squares best fit lines...

SJK 18:43, 18 December 2008 (EST)
18:43, 18 December 2008 (EST)
Nice graphs and good linear regression.
1st Order Trial 1 1st Order Trial 2
2nd Order Trial 1 2nd Order Trial 2

 Data Summary Planck's Constant h = (4.29 ± 0.19)e-15 [eV s] % error = 3.6 % Work Function ω0 = 1.51 ± 0.13 [eV] % error = 11.0 % accepted h = 4.14e-15 [eV s] accepted ω0 = 1.36 ± 0.08 [eV]

## Conclusion

I am very satisfied with our results. I was initially worried that some odd fluctuations in our data was going to effect our outcome, but it turns out those fluctuations were so miniscule it had little effect. My error is somewhat larger than one could hope, but to have only a 3% error from the actual on my final data makes me quite happy.

The experiement was certainly one of my favorites, it put me right there in Quantum history at the very roots of the new paradigm of Physics.SJK 18:40, 18 December 2008 (EST)
18:40, 18 December 2008 (EST)
Great! I really like this one also.