# User:Manuel Franco Jr./Notebook/Physics Lab 307/2008/11/12

Planks Constant Lab Main project page
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SJK 15:19, 17 December 2008 (EST)
15:19, 17 December 2008 (EST)
Excellent data and analysis notes!

# Planks Constant

Lab Partner: David

## Objectives

1. Understand the Photon Theory of Light
2. Understand Particle/Matter Interaction
3. Determine Planks Constant h

## Materials

• There are 3 filters:
1. Relative Transmission (Ranges from 100% to 20%)
2. Mercury Yellow Line
3. Mercury Green Line
• Wavetek 85XT RMS DVM (Digital Volt Meter)
• PASCO AP-9368 h/e apparatus with two 9V batteries (See link under Equipment) [1]
2. white photo diode
3. Light Shield
• Hg lamp: (Light Source Os-9286 by PASCO Scientific) | Line voltage Range 108-132 in vacuum | Power: 125 W max Freq. 47-63 HZ 115 V
• Lens/grating assembly

## Setup

The connections are simple. We plugged in the Hg lamp to the wall socket, and plugged the Voltmeter to the h/e apparatus, and aligned the lens to get the sharpest image on the mask. The batteries were already in the h/e apparatus. (NOTE!! Check batteries with volt meter to see if they are usable!)

## Procedure

### Part 1: Measuring the Charge Rate

We turned on the Hg lamp and let it heat up. Then we set the lens where the image was sharpest on the white mask. The two filters are used corresponding to the color on the white mask: green to green and yellow to yellow. So for the first set of data we used green. We set the green filter on the white reflective mask, and made sure that the color and the aperture were lined up with green being as sharp as possible. The transmission filter allows a X% of light to pass through. We then repeated this process for yellow.

### Part 2: Determining h

We made sure that the focus and alignment were fine. We now had to fine the stopping potential for each of the first order and second orders colors of Hg. We started from ultraviolet and stopped at yellow, and ended up with a total of five colors for each order. For more details refer to the Lab Manual (Sections 5.5) and images

## Data

### Part 1

Green Filter/Green Light

Relative Tran. Voltage Time 1 Time 2 Time 3 Time 4 Time 5
Relative Tran. 100% .883 +/- .001 V 14.97s 14.06s 16.41s
Relative Tran. 80% .884 +/- .001 V 16.9s 13.4s 15.78s 12.75s 13.16s
Relative Tran. 60% .883 +/- .001 V 25.8s 19.75s 18.31s 17.72s
Relative Tran. 40% .882 +/- .001 V 28.44s 23.66s 16.56s
Relative Tran. 20% .882 +/- .001 V 84.44s 29.25s 50.00s

Yellow Filter/Yellow Light

Relative Tran. Voltage Time 1 Time 2 Time 3
Relative Tran. 100% .740 -/+ .001 V 15.40s 18.09s 17.22s
Relative Tran. 80% .740 -/+ .001 V 17.88s 15.53s 16.69s
Relative Tran. 60% .738 -/+ .001 V 22.85s 18.41s 22.50s
Relative Tran. 40% .735 +/- .001 V 28.56s 24.19s 27.00s
Relative Tran. 20% .735 +/- .001 V 45.40s 46.50s 49.35s

In the first data table, we took a couple of more measurement because the time was not consistent. As for those that were consistent, we only took three measurements. The second set of data came out consistent.

### Part 2

Measurements of 1st order

Color Measurement 1 (V) Measurement 2 (V) Measurement 3 (V) Measurement 4 (V) Measurement 5 (V)
Ultraviolet 2.0655 +/- .0005 1.8595 +/- .0005 1.6435 +/- .0005 1.6515 +/- .0005 2.1 +/- .1
Violet 1.6575 +/- .0005 1.5745 +/- .0005 1.4025 +/- .0005 1.4065 +/- .0005 1.708 +/- .001
Blue 1.4345 +/- .0005 1.3755 +/- .0005 1.2375 +/- .0005 1.2325 +/- .0005 1.491 +/- .001
Green w/ filter .8035 +/- .0005 .7875 +/- .0005 .7385 +/- .0005 .7415 +/- .0005 .851 +/- .001
Yellow w/ filter .6775 +/- .0005 .6785 +/- .0005 .6315 +/- .0005 .6305 +/- .0005 .714 +/- .001

After talking to Dr. Koch, we come the realization that our voltage is too small, some of our data is not correct. See below for the unused and used data. (Section: Data Analysis, Part 2)

Measurements of 2st order

Color Measurement 1 (V) Measurement 2 (V) Measurement 3 (V) Measurement 4 (V)
Ultraviolet 1.665 +/- .005 1.6435 +/- .0005 1.6395 +/- .0005 1.6385 +/- .0005
Violet 1.5395 +/- .0005 1.4845 +/- .0005 1.4505 +/- .0005 1.4315 +/- .0005
Blue 1.4715 +/- .0005 1.4175 +/- .0005 1.3745 +/- .0005 1.3575 +/- .0005
Green w/ filter 1.1115 +/- .0005 1.1145 +/- .0005 1.1095 +/- .0005 1.1075 +/- .0005
Yellow w/ filter .6755 +/- .0005 .6835 +/- .0005 .6855 +/- .0005 .6885 +/- .0005

## Data Analysis

### Part 1

#### Data Table and Graphs

Here is the spreadsheet for this section.

SJK 15:12, 17 December 2008 (EST)
15:12, 17 December 2008 (EST)
Nice graphs and use of SEM.
Relative Transmission Exp. Value Green Exp. Value Yellow
100% 15.147 +/- .684 s 16.903 +/- .793 s
80% 14.398 +/- .819 s 16.700 +/- .678 s
60% 20.395 +/- 2.138 s 21.253 +/- 1.425 s
40% 22.887 +/- 3.451 s 26.583 +/- 1.179 s
20% 54.563 +/- 16.095 s 47.083 +/- 1.177 s

#### Analysis

The passing of different amounts of the same colored light through the variable transmission filter has effects on the stopping potential, and also on the maximum energy of the photoelectrons, as well as the charging time after pressing the discharge button. The data and graph show that as the percent of the relative transmission decreased, and the time elapsed increased. Also, the voltage was held constant aka stopping potential. So what does data mean? The R.T. filter filters the number of photons that passed through. So if the R.T. filter is at 100%, most, if not all of the photons are getting through. If more photons get through the less time it takes for the photoelectric effect to reach that constant stopping potential.

The different colors of light had other effects as well as on the stopping potential and also on the maximum energy of the photoelectrons as mentioned earlier. In the case of green compared to yellow, green has a wavelength of approximately 495–570 nm and yellow has a wavelength of aproximately 570–590 nm, green has lower wavelength; thus a higher frequency by this realtion: λ=1/f. Quantum theory predicts "that higher frequency light would produce higher energy photoelectrons, independent of intensity, while increased intensity would only increase the number of electrons emitted (or the photoelectric current)." Lab Manual (Section: 5.2.2 The Photoelectric Effect) That would explain why the base voltage for green (0.883 +/- .001 V) is higher than the base voltage for yellow (0.738 +/- .001).

According to classical mechanics, it "predicts that as the intensity of incident light" increases, "the amplitude and thus the energy of the wave would increase." Lab Manual (Section: 5.2.2 The Photoelectric Effect) But we did not increase the intensity or brightness of the Hg lamp. It was held constant and the voltage changed based on the color/frequency. So, this experiment supports a wave or a quantum/photon model of light.

The data shows that there is a small decrease in the voltage for both green and yellow. The voltage for green drops from .883 +/- .001 V to .882 +/- .001 V, and yellow drops from .740 -/+ .001 V to .735 +/- .001 V. Quantum theory states that the stopping potential does NOT depend on the intensity, so this change could be a result of a leak somewhere in the circuit. That is why there is a slight drop in the measured stopping potential as the light intensity is decreased.

### Part 2

#### Data and Graphs

I used the frequencies from this table in the manual to plot and determine h.

In order to have four graphs as instructed by the manual, we took our best measured data from section: Data, Part 2.

Measurements of 1st order

Color Measurement 1 (V) Measurement 5 (V)
Ultraviolet 2.0655 +/- .0005 2.1 +/- .1
Violet 1.6575 +/- .0005 1.708 +/- .001
Blue 1.4345 +/- .0005 1.491 +/- .001
Green w/ filter .8035 +/- .0005 .851 +/- .001
Yellow w/ filter .6775 +/- .0005 .714 +/- .001

Measurements of 2st order

Color Measurement 1 (V) Measurement 2 (V)
Ultraviolet 1.665 +/- .005 1.6435 +/- .0005
Violet 1.5395 +/- .0005 1.4845 +/- .0005
Blue 1.4715 +/- .0005 1.4175 +/- .0005
Green w/ filter 1.1115 +/- .0005 1.1145 +/- .0005
Yellow w/ filter .6755 +/- .0005 .6835 +/- .0005
SJK 15:18, 17 December 2008 (EST)
15:18, 17 December 2008 (EST)
Good job citing Arianna. Your data have the 2nd order green problem...thus invalidating the 2nd order measurements and making the weighted average invalid as well...though it's good you learned how to implement it.

I followed Arianna Pregenzer-Wenzlers excel sheet to calculate h and Wo, their error, and their weights. Here is the data analysis spreadsheet for this section.

#### Analysis

These are my calculations for h and Wo, their accepted values, and comments:

1. My experimental value for h: (4.55 +/- .16) x 10^-15 eV*s
2. My experimental value for Wo: 1.642 +/- .092 eV
3. Current accepted value of Planks Constant: 4.135669212e-15 ± 1.2407e-21 eV*s
4. Accepted Value of the Work Function: (1.36 +/- .08) eV
5. Percent Difference in h: 10.05 %
6. Percent Difference in Wo: 17.22 %

My experimental values with its uncertainties is no were near the accepted values plus their uncertainties in both cases. The apparatus was acting up on my lab partner and I. The voltage was changing on us. It was not the small changes due to leak of current, it was some kind of malfunction. The voltage dropped was we continued to take measurements as recorded in the 2 set of data. It dropped from 2.0 V to 1.6 V which gave us a experimental error. Although, we did filter out the data, I feel that we could of taken better measurements.