Physics307L:People/Le/Notebook/071001

Calculations
--Linh N Le 15:54, 1 October 2007 (EDT)

Part 1
In the first part of the lab, we measured the time it took to return to a certain % of the stopping potential for different wavelengths of light and for different intensities of said light. Since light acts like a particle, we surmised that halving the intensity of the light (thus halving the amount of packets that enter) would double the rise time.

UV Light
http://openwetware.org/images/f/ff/Uvplot.jpeg

As we can see, from 100% intensity to 40% intensity, the rise time only increased very slightly. This could have been a problems with the fact that our intensity filter, filtered out UV light.

Blue-Violet Light
http://openwetware.org/images/f/fe/Bluevioletlight.jpeg

It too, is not linear. It actually looks more exponential. The graph for Blue light is the same shape as the UV light, although the scale is different.

Green Light
http://openwetware.org/images/2/23/Greenlight.JPG

Once again, an "exponential" looking plot.

Yellow Light
http://openwetware.org/images/6/6b/Yellowlight.JPG

Woah! That's some weird looking data. Our apparatus was having trouble at the very end of the experiment last week, so we are going to retake this data.

http://openwetware.org/images/2/29/Yellow2.JPG

This one looks more consistent with the rest. I would like to note that 60% is still a smaller time than 80% and 40%. This happened twice.

Part 2
In this part, we find Planck's Constant and the work function of the apparatus using our stopping potential, the frequency of the light and plotting the linear function:

$$K=h \nu - \phi$$

Where K is the kinetic energy of the electrons popped off, h is Planck's constant(found by slope of graph), $$\nu$$ is the frequency of the light and $$\phi$$ is the workfunction of the metal(found by y-intercept of graph).

Wavelengths and frequencies taken from last year's lab notebook

According to this website:http://dev.physicslab.org/Document.aspx?doctype=3&filename=AtomicNuclear_PhotoelectricEffect.xml

We can calculate the KE of the electron by multiplying the charge of an electron by the stopping potential, plot all our KE's vs Frequencies and using the slope and Y intercept, find the values we want

Example Graph: Photoelectric Effect/Stopping Potential Relations

UV
Wavelength about 365nm

Frequency about 8.2E14 Hz

Stopping Potential(1) 2.06

KE(1)=3.300E-19J

Stopping Potential (2) 2.07

KE(2)=3.316E-19J

Avg Stopping Potential 2.065V

Avg KE=3.308E-19J

Blue-Violet
There were 3 lines, blue, indigo and violet. We picked the middle line, indigo.

Wavelength about 420nm

Frequency about 7.14E14 Hz

Stopping Potential (1)1.76V

KE(1)=2.819E-19J

Stopping Potential (2)1.76V

KE(2)=2.819E-19J

Avg Stopping Potential: 1.76V

Avg KE=2.819E-19J

Green
Wavelength about 546nm

Frequency about 5.48E14 Hz

Stopping Potential (1).89V

KE(1)=1.43E-19J

Stopping Potential (2).86V

KE(2)=1.377E-19J

Avg Stopping Potential=.875V

Avg KE=1.40E-19J

Yellow
Wavelength about 578nm

Frequency about 5.18E14 Hz

Stopping Potential(1):.75V

KE=1.20E-19ev

Stopping Potential:.76V

KE=1.21E-19ev

Stopping Potential:.75V

KE=1.209E-19ev

Taking the KE's from the first order voltages
http://openwetware.org/images/9/95/Placks_1.JPG

Y intercept=workfunction=2.484E-19 J

Slope=Planck's Constant=7.18E-34Js

Taking the KE's from the 2nd order voltages
http://openwetware.org/images/5/59/Plancks_2.JPG

Y intercept=workfunction=2.563E-19 J

Slope=Planck's Constant=7.29E-34Js

Taking the average of the voltage, to find the average KE
http://openwetware.org/images/f/f0/Plancks.JPG

The Y-intercept=workfunction=is 2.504E-19 J

The slope is =Planck's Constant = 7.21E-34 Js

Error Analysis
Mean of Planck's Constant= $$\frac{7.21x10^{-34} + 7.29x10^{-34} + 7.18x10^{-34}}{3}=7.22x10^{-34}$$

Standard Deviation $$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}.$$

$$\sigma = 4.64 x 10^-{36}$$

Standard Error :$$ s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} $$

s= $$5.68x10^{-36}$$


 * $$SE = \frac{s}{\sqrt{N}}

$$

$$SE=3.28x10^{-36}$$

$$%error= \frac{|Actual-Experimental|}{|Actual|}x100$$

Using the Mean for Planck's

$$%error=9.06%$$

Sources of Error

 * Light from outside can enter the apparatus and skew the light we are measuring
 * Although using a filter for green and yellow, it is not a perfect filter and other colors of light may still get through
 * The voltmeter may not be 100% accurate (it showed a .04V even while not connected to anything)

Summary
You can find the first week's work here. This is where the procedure and initial data were taken.

As for the lab as a whole, there was not alot of error to be found. The big sources and some data analyses are listed above. Since there was not alot of "interaction" I feel that this lab was a bit lacking. I had very little control on how things were measured.

Although the design was ingenous, I would have liked to do this lab "the old fashioned way" (ie turning a dial that adjusts the voltage and finding the stopping potential where current=0).