User:John Callow/Notebook/Junior Lab 307/2009/11/11

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Plank's constant
Link to my summary

Dr. Gould's manual

For Experimenters
The light source is high voltage, but the user is protected pretty well from anything.

The light source does give off ultraviolet radiation, I'd suspect it is far less harmful than laying in the sun but to be safe just point it away.

For Equipment
Disconnect the input power before changing the bulb.

Don't turn the lamp on if the bulb looks damaged.

Turn on the lamp 20 minute before use and don't turn the lamp on and off over and over in short periods of time.

equipment
(1) Pasco scientific Hg Light Source OS-9286 h/e apparatus

(1) yellow filter

(1) green filter

(1) variable transmission filter

(1) multimeter

(2) banana cables

Setup
Turn on the light source and let it warm up for five minutes. While it's heating connect the multimeter to the outputs on the h/e apparatus. Once the lamp is warmed up a little and easily viewable slide the lens/grating back and forth till the position is found that best focuses the light on the h/e apparatus. Then open the light shield on the h/e apparatus and if everything is working it should be good to start taking data.



Experiment 1: The Photon Theory of Light
This experiment's purpose is to verify the photon theory of light by showing that the maximum kinetic energy of photo-electrons depends on the frequency of incident light but does not depend on intensity. To test this we look at the stopping potential of several colors (different frequencies of light) and then using the intensity filter observe whether these potentials change with different intensities.

Taking Data
To find the stopping potential align so the color of light is lined up with the slit in the apparatus, make sure the lights are off, hit the zeroing button on the apparatus, and then wait for the reading to stabilize on the multimeter. For the green and yellow lines, use the corresponding filters as there is a lot of overlap. The manual does not mention the red lines but we attempted to measure them anyways. We found that there must be a lot of overlap likely between the red and ultraviolet in the area. We didn't have an actual filter for red, but we tried using some cheap 3D glasses which while didn't do a great job of blocking out the ultraviolet, it gave good reason to believe that there was overlap. The stopping potential decreased significantly, and we no longer had an issue of low frequency light carrying about the same energy as ultraviolet. Though we already knew that this would be the case, if we hadn't known this and where originally trying to give evidence of the theories above using this experiment this would have been a major problem. We felt it would still be a good idea to find a reason for why the red area was such a trouble spot though.

Data
This data shows pretty good evidence that changing the frequency of light changes the stopping potential.

The stopping potential barely changes when intensity is turned down and so likely has no effect other than increasing charge time. The slight drop intensity is because the apparatus naturally discharges at a certain rate, and as the charge rate becomes slower the discharging begins to have a larger effect on the measurement. So all of our readings would actually be a little higher, but with 100% intensity the discharge rate would have little effect in the final outcome as the charge rate is so high up until right before the max.

plots
For these plots I believe the fit should be like 1/x. When intensity is high, the charging time is low. As x-> 0 however charging time should head to infinity. I could not find a direct way to do this so I just took 1/intensity vs. time which ended up looking linear, found a linear fit, then flipped my intensity back.

As another side experiment we wanted to compare the charging times measured to 100% and 90% and see which fits the behavior we expect. The problem with 100% is because slight uncertainty in the multimeter leads to terrible data. Being just slightly off, we could have sat there for an eternity waiting for the charge to reach what we measured as the maximum, especially at low intensity. And the problem is, at 100% and low intensity we expect it to take 2-3 minutes to fully charge and it is very easy to sit and wait for a bit only to end up with the multimeter either never recording the max or being slightly off and adding 1-2 minutes to the charge time. This method is frustrating and slow, and from the plots below seems to do a poor job demonstrating how charging time behaves as a function of intensity.

For the purposes of experiment we were really only after proof that after a given time the charge is the same at all intensities it just takes longer to reach the max, and the 100% method is fine for this. But if we had any interest in more accurate behavior of the charging I believe that the 90% method gives a better picture. For proof we really only needed to compare the max potentials found at each wavelength and at different intensities, but taking this data did force us to think of ways to measure it and this will hopefully help make an informed decision on how to take data in future experiments where the charge time is more important.

For the 100% plot of violet(blue) I found that

$$ 100% Charging Time = \frac{1472.8}{intensity} $$

with uncertainty of the fit being 208.7

For 90%

$$ 90% Charging Time = \frac{95.6}{intensity} $$

with uncertainty of the fit being 9

For the 100% plot of deep violet I found that

$$ 100% Charging Time = \frac{4090.6}{intensity} $$

with uncertainty of the fit being 363.3

For 90%

$$ 90% Charging Time = \frac{334.5}{intensity} $$

with uncertainty of the fit being 21.6

The plots for 90% looks better to me for the most part. A big advantage to 90% that we didn't get to show is that we could take about 5 measurements in the time it takes 1 going to 100% which would allow for using the mean and error bars to see which points are outliers and such. The 100% method still looks fine for deep violet, but in violet(blue) the problems of that method and the uncertainty in the multimeter caused one of our measurements to be likely way above what it should be. This would likely be fixed by taking multiple measurements, but the thought of taking multiple several minute long measurements that we aren't even sure the multimeter will ever reach the charge we're after is unpleasant which is why we explored the 90% method.

I'm also pretty sure the two different methods could be directly compared but I'm getting tired, they look to be following the same type of curve though. I have lots of time this weekend so I might try and update this a little more. I'd especially like to update a few things with more data if the lab I do this week goes well and I have 20 minutes to get some more from this lab. More on that is discussed in part 2.

Formulas
From the lab manual we have $$ E = hv = K{E_m}+{W_0}$$

where h is planks constant, v the frequency, E the total energy, $$ K{E_m}$$ the maximum potential energy of emitted electrons, and $${W_0}$$ the work function. From | Anastasia Ierides' notes

$$ e*{V_s} = K{E_m} $$

which plugging into the first formula and solving for the negative potential to stop the electrons $$ {V_s} $$ results in

$$ {V_s} = \frac{hv - {W_0}}{e} $$

which is of the form

$$ {V_s} = Av+ B $$

Where A and B are constants that will be solved for when doing the linear fit.

plot
We ran out of time and only got the first order measurements done.(Part of this is that I think we forgot that we needed the second order measurements during the frustration with the multimeter and finding a better way to view the rate of charge.) It would only take about 15 minutes to get the rest so we should have time assuming this weeks lab goes well.

The manual asks for a different plot for each measurement trial. I'm going to assume that it is better to instead take the mean of all our measurements and use sdem to plot error bars instead.



So from the linear fit I have

$$ Stopping potential = 4.48*{10^{-15}}*Frequency-1.58 $$

With uncertainty in the slope being 7*10^-17 and constant term .05.

From the formulas section we relate $$ 4.48*{10^{-15}} = \frac{h}{e}$$ and $$1.58 = \frac{W_0}{e}$$

Using that $$e = 1.602*{10^{-19}} Coulombs$$ we have that

$$ h = 7.18(11)*{10^{-34}} Js $$ and

$$ {W_0} = -2.53(8)*{10^{-19}} J$$

The yellow
A large majority of our time was wasted trying to measure the stopping potentials at different intensities for yellow. What ended up happening over and over is as we used the intensity filter to lower the intensity, stopping potential would shoot up at and past the 60% setting. After many attempts we came to the conclusion that the intensity filter must be diffracting either the green or other yellow (the two yellow bands aren't really distinguishable but the manual says there is two). After spending a good hour investigating the issue we decided to try the blue and deep violet to see if any problems arose there. There isn't any nearby bands for these, and as we suspected there was no issue which is mostly what led us to our conclusion. There are some other ideas, we could have been slightly moving the apparatus when changing intensities. But we even tried placing my modern physics book down to try and lower the amount of movement when intensities were changed and still had the same result.

It was an interesting issue, but we probably should have just moved to the violets sooner so we didn't run out of time.

multimeter
Our original multimeter ended up being a problem. Measurements on the lower wavelengths just didn't seem to want to be consistent. After trying to block any other sources of light in the room with a physics book we finally decided that our multimeter was the problem. After switching to what looked like a fancier multimeter our readings stopped jumping around so much.

sources of error
Probably the main source of error was just random background light. We minimized this using a book and that seemed to do a pretty good job. Other than that the yellow and green would change by a lot if alignment was just a little off. The filters didn't seem to be working very well. We tested them to see how well they'd block just the ultraviolet alone and found they didn't seem to do to well.


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