User:Arianna Pregenzer-Wenzler/Notebook/Junior Lab/Planck's Constant Summary

Planck's Constant Summary

 * My Course Page

Brief summary
look up Planck's Constant in lab manual linked below, to see what was basically required for this lab.
 * lab manual.


 * notebook entry for Planck's Constant lab

In this experiment we used a mercury vapor light source and an insturment refered to in the lab manual as the h/e apparatus to measure and compare the stopping potential of...

i) the same band in the mercury spectrum at differing intensities

ii) the different bands in the mercury spectrum (1st and 2nd order)

Analysis (Experiment I)

 * plot charging time results

[[Media:Planck's Constant I final.xls]]

In excel I ploted the average time it took to reach Vmax, vs the Vmax for each intensity of Blue I (which is the UV line) and of Blue II (which is refered to as the violet line in the lab manuel). I included on the spread sheet the standared deviation for each averaged time and the standared deviation of Vmax for the two color lines.


 * describe effect of intensity on Vmax and on charging time

Blue I

average Vmax: 1.95V

STD: 0.019026V

SEM: 0.008509

Blue II

average Vmax: 1.6158V

STD:0.011946V

SEM:0.005342

Because Vmax varies so little between 100% and 20% intensity I would conclude, in light of the data we collected, that Vmax does not depend on the intensity.

When looking at the effect of the intensity of the light on charging time, the trend seemed to be that as intensity decreased, charging time increased (which is the expected result). But if you look at our data you will see that this isn't always the case, for both Blue I and Blue II it took less time on average to reach Vmax at 60% intensity than at 80%. Also the greatest inconsistancy in our data is the time required to reach Vmax, the SDT of the average time is, in the majority of the trials, quite large.


 * describe effect of frequency (or Emax (hν)) on Vmax

According to our data, the shorter the wavelength (or the higher the frequency) the greater the stopping potential (Vmax) of that color. If you look at our data you will see the the greates Vmax corresponds to Blue I (the UV line) which has a frequency,ν≈8.2E+14, and the smallest Vmax corresponds to Orange (yellow according to the manuel) which has a frequency, ν≈5.1E+14. This was one trend that was consistant through out the data we collect in this lab.


 * do results support wave or photon model of light?

I would say that our results definitely support the photon (quantum) model of light in that our data shows that an increase in the frequency of the light is what leads to a greater stopping potential, not an increase in intensity. I would not say that you could conclude from our data that the number of electrons (the photoelectric current) increases with increased intensity, because there was too much deviation in our data concerning the time it took to reach Vmax at a given intensity to draw any meaningful conclusions.


 * explain slight drop in Vmax corresponding to a decrease in intensity

According to section 5.6 (thechnical information on the h/e apparatus) in the Planck's Constant lab (see lab manual), the h/e apparatus has a high impedance amplifier that allows us to measure Vmax with a voltmeter. The hight impedance means that the voltage coming in equals the voltage going out, ie. a photoelectric current comes in, goes out unchanged and gets measured by the voltmeter and we record Vmax. While the apparatus is good it is not perfect and as the amount of time necessary to charge the capacitor increases there is some current drain which leads to a decrease in Vmax as intensity decreases.

Note:

We looked at the wave form the voltage going from zero to Vmax using the osciliscope, and got the attached picture. You can see there is an initial spike in voltage greater in height to Vmax that corresponds with the release of the discharge (zero) switch on the h/e apparatus (something else I learned reading section 5.6) and allows the apparatus to begin building up charge, then the voltage dipps and grows again in the expected exponitial fassion, something like 1-e-x until it reaches Vmax. In this picture I'm not sure if the voltage made it all the way to Vmax, we froze the image before the constant max voltage really got established. So the increase in voltage as is approaches Vmax follows the expected curve, but it reaches Vmax so quickly (the time it took to form the picture shown bellow couldn't have been more than a second or two, maybe less) that given the methods we were using in this lab to measure charging time we were inbarking on an impossible task from the begining and its no wonder that our data in that area was inconclusive.



Analysis (Experiment II)

 * plot results of all four trials

Knowing that I want to use the equation (Energy) hν = KEmax + W0 to solve for Planck's constant h, and W0 where KEmaxis equal to Vmax, I rearranged this equation to read Vmax = hν - W0. Then I ploted frequency vs Vmax so that the slope of the linear least squares fit line would be the value of Planck's constant h, and b = W0.


 * perform a linear least squares fit on each data set

I used an Excel function to calculate least squares fit for h and W0 along with their error for each trial.

[[Media:Planck's Constant IIfinal.xls]]


 * calculate an experimental value for h and W0 as a weighted average, include error

With the help of Dr Koch, I got a formula for the weighted average for the four trials. The weighted average is an average of the four values of h and W0 that 'wieghts' the each separate value depending on its error (ie; it distance from the best fit line). Dr Koch left it to me to find out how to deal with the error, but though I found information on least square fitting least squares fit and how to calculate a weithted average, I found nothing I could quickly understand on how to deal with error (I did find a good section on error propagation, but I didn't know how to apply it). Bellow are my weighted averages for h and W0 along with their respective error, but the listed error is just the SEM of the error of the four trials. The actual error should be less, since the final calculated values of h and W0 are more dependent on the values that contained the least amount of error (deviate least from the best fit line), this is an area where I have more to learn.

h = (4.08016 ±0.139)E-15 eV*s
 * Steve Koch: This would be easier to read (and thus better written) as:
 * h = (4.08 +/- 0.14) E-5 eV*s

W0 =(1.59163 ± 0.09415) V
 * Steve Koch: Same for this one
 * W = (1.59 +/- 0.09) V


 * compare with accepted value of h

Planck's constant, h = 4.135667E-15 eV*s

I'm not sure if I'm looking at this correctly, but it seems like the value of h that I calculated using my experimentally collected data compares well with the accepted value of h becaues if you look at our value along with its error it overlaps the accepted value.


 * comment on quality of results

I am surprised, because if I am looking at my calculated data correctly we actually got fairly acurate results, and I was expecting to be pretty far off, because systematic error.

What I Learned
I learned alot this lab, mainly sitting right here working with Excel. I learned how I should enter my data so that it can be easily manipulated and read (look at the difference between the spread sheets for experiment I and II). I learned that to veiw a waveform on an oscilliscope use DC coupling, and that the 1/V on the voltmeter is an indicator as to how precisely the insturment is measuring voltage (not an indicator to divide all measurments by 20). I learned that I need to buy one of those data analysis books over break, because data manipulation is a whole other kind of math and I would like to have a better refrence than what I get drifting around the internet. *Arianna Pregenzer-Wenzler 01:23, 15 October 2008 (EDT):