# Planck's Constant

To view the exact procedure for this lab or to learn more about the apparatus follow the given link to last year's manual.Physics 307 Lab Manual also our data can be found at my notebook

## Purpose

"The emission and absorption of light was an early subject for investigation by the German physicist Max Planck. As he attempted to formulate a theory to explain the spectral distribution of emitted light based on a classical wave model, he ran into considerable difficulty Classical theory (Rayleigh-Jeans Law) predicted that the amount of light emitted from a black body would increase dramatically as the wavelength decreased, whereas experiment showed that it approached zero. This discrepancy became known as the ultraviolet catastrophe. Experimental data for the radiation of light by a hot, glowing body also showed that the maximum intensity of emitted light departed dramatically from the classically predicted values (Wien’s Law). In order to reconcile theory with laboratory results, Planck was forced to develop a new model for light called the quantum model. In this model, light is emitted in small, discrete bundles of energy or quanta, later called photons. The relationship between the classical and quantum theories for the emission and absorption of light can be investigated with our apparatus. In combination with a mercury vapor light source an accurate determination of the ratio h/e and thus of h, Planck’s constant, is possible. This constant has turned out to be one of the most important fundamental constants in all of modern physics.

Planck’s constant was found to have significance beyond relating the frequency and energy of light, and became a cornerstone of the quantum mechanical view of the atomic and subatomic world. In 1918 Planck was awarded the Nobel prize for introducing the quantum theory of light."(1)

"In this lab we will be using an Hg vapor light source to ultimately determine the value of Planck's constant. In addition, we will look into the differences between the classical and quantum perspectives of light. In Experiment 1 we look at different intensities of light, which according to the classical model should be the main determination in a photons maximum kinetic energy. Our findings, however, should prove the quantum perspective that a photons energy is based only on it's frequency."(2)

## Equipment and Setup

Our experimental setup includes a mercury vapor light source, an h/e apparatus, and a digital voltmeter. At one point we also used an oscilloscope for our data collection (more on this in the Conclusions section). To properly measure the yellow and green lines a filter will be necessary. Experiment 1 also requires the use of a relative transmission filter in order to measure different intensities.(2)

## Experiment 1

SJK 03:02, 29 November 2007 (CST)
03:02, 29 November 2007 (CST)
Why should you use linear fits here? What relation would you expect?

The h/e apparatus collects the monochromatic light from the Hg vapor light source and the associated photoelectrons are ejected from the cathode to the anode. This slight current eventually stops and the anode-cathode potential stabalizes. In this part of the experiment we will be measureing the time it takes to reach this point.

### Yellow Emission Line

Stopping Voltage 0.724V

 Trans % Time 1 Time 2 100% 8.3s 9.2s 80% 11.5s 11.4s 60% 16.5s 16.9s 40% 18.0s 19.2s 20% 43.4s 40.6s

### Green Emission Line

Stopping Voltage 0.849V

 Trans % Time 1 Time 2 100% 6.9s 7.5s 80% 8.7s 8.7s 60% 12.0s 11.2s 40% 19.9s 19.0s 20% 31.6s 30.2s

### Conclusions

#### Part A

Looking at previous labs we assumed we could use the oscilloscope to take fall time measurements, but after setting it up and reading further into the manual we found that the time that we were looking for was outside of the resolution of the scope. After we go that figured out we were able to take data for the fall times above showing a definite trend in the data. We saw that the amount of time it takes for the voltage to build up was dramatically longer with decreasing intensity. The procedures can be found in the manual for the device at:

#### Part B

Analysis

1. The amount of light doesn't seem to effect the stopping voltage, but does seem to effect the time it takes to reach the stopping potential. This tells us that the intensity will effect the amount of electrons stimulated but not their maximum energy.

2. The color of light does effect the max energy of the photoelectrons and does seem to be linearly related.

3. The experiment defends a quantum model of light.

## Experiment 2

In this portion of the experiment we measure the stopping voltage associated with a given wavelength of light. This relationship should give us what we need to determine the value of h.

### 1st Order

Color (1st order) Potential 1 (Volts) Potential 2 (Volts)
Yellow .724 .720
Green .859 .869
Blue 1.502 1.510
Violet 1 1.732 1.720
Violet 2 2.078 2.078

### 2nd Order

Color (2nd Order) Potential 1 (Volts) Potential 2 (Volts)
Yellow .778 .786
Green 1.255 1.270
Blue 1.574 1.583
Violet 1 1.735 1.752
Violet 2 2.064 2.086

### Calculations

The value of h is determined by preforming four least square fits to the collected data points for both first and second order. The slope of this line gives the ratio of h/e. At this point I chose to summarize my data for the first and second order data separately after seeing a fairly large discrepancy between the two sets. Here then I have the derived values of h for both first and second order.

#### Final value for h 1st order

$7.2311(+/-.039)\times10^{-34}(J*s)$

standard deviation of 3.854E-36

standard error of +/-1.839E-36

#### Final value for h 2nd order

$5.944(+/-.026)\times10^{-34}(J*s)$

standard deviation of 2.601E-36

standard error of +/-2.724E-36.

### Conclusions

SJK

Comparison to accepted values?

Our first and second order data if averaged together would have given us a number that was closer to the accepted value but this didn't make sense. We expected the data to be a lot closer between the two sets and therefore it didn't seem right to use them together. There seemed to be some sort of systematic error in one or both of our data sets.

## References

(1) Physics 307L: Lab Book, 14 July 2006, Professor Micheal Gold, <http://www-hep.phys.unm.edu/%7Egold/phys307L/manual.pdf>

(2) "Physics307L:People/Ritter." OpenWetWare, . 4 Nov 2007, 22:08 UTC. 13 Nov 2007, 20:32 <http://openwetware.org/index.php?title=Physics307L:People/Ritter&oldid=164425>.