User:David E. Sosa/Notebook/2008/11/12

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Plank's constant Experiment Notes.

To do list:

  • Identify security issues.
  • Read the lab manual. (Done)
  • Read article in Wikipedia
  • Read past experiments related to this one.
  • Identify the kinds of analysis that are going to be used in this lab.
  • Check the two battery voltages.

Equipment

  • PASCO AP-9368 h/e Device
  • 2 9V OP-Amp Batteries
  • PASCO OS-9282 Scientific Hg Light Source
  • Tektronix TDS 1002 Digital Oscilloscope
  • Wavetek 85XT RMS DVM

Some formulas for later

Equations

In effect quantitatively using Einstein's method, the following equivalent equations are used:

Energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron

Algebraically:

bd44368c6a5fe759a79feb0cac2e05a4.png

where

  • b0f540b2cf63fcb37995455670be5cbd.png is Planck's constant,
  • f is the frequency of the incident photon,
  • \phi = h f_0 \ is the work function (sometimes denoted W instead), the minimum energy required to remove a delocalised electron from the surface of any given metal, E_{k_{max}} = \frac{1}{2} m v_m^2is the maximum kinetic energy of ejected electrons,
  • f0 is the threshold frequency for the photoelectric effect to occur,
  • m is the rest mass of the ejected electron, and
  • vm is the speed of the ejected electron.

Since an emitted electron cannot have negative kinetic energy, the equation implies that if the photon's energy (hf) is less than the work function (φ), no electron will be emitted.


Data

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

Ultraviolet Light

Relative Tran. Voltage Time 1 Time 2 Time 3 Time 4
Relative Tran. 100% 1.6585 -/+ .0005 V 18.91s 17.18s 17.11s
Relative Tran. 80% 1.6735 -/+ .0005 V 27.30s 26.25s 30.69s
Relative Tran. 60% 1.6545 -/+ .0005 V 36.56s 30.35s 31.09s
Relative Tran. 40% 1.6795 +/- .0005 V 34.35s 37.22s 35.91s 37.90s
Relative Tran. 20% 1.6715 +/- .0005 V 74s 72s 76.09s

Manuel and I think it is a good idea to stay around 20 minutes after next class to take a few more measurements to improve the analysis. Since we already have the data analysis done, it will be quick and easy to introduce the new numbers and get an improved result.

Determination of h

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 taking several measurments something strange happended with the voltmeter. The measurments started to drop from their previous values. We could not explain why this was happening, but we decided to carry on with the measurments and perform the data analysis later to get a better perspective on the results.

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


Manuel 4:29 pm, 19 Nov 2008 (EDT): So here is the link to my raw data

Manuel and I think it is a good idea to stay around 20 minutes after next class to take a few more measurements to improve the analysis. Since we already have the data analysis done, it will be quick and easy to introduce the new numbers and get an improved result.

Results and Analysis

Even though we are going to take some more data, I think it is convenient to do some analysis now so when the new data comes in, we can just plug in.

Experiment #1 (The Photon Theory of Light)

Analysis for part #1 Image:Plank's Contant Part 1-1.xls

Green Line with Green Filter

  • Average maxV:0.8821 V
  • STD:0.00083666
  • SEM:0.000374166

Yellow Line with Yellow Filter

  • Average maxV:0.8821 V
  • STD:0.00083666
  • SEM:0.000374166

Ultraviolet

  • Average maxV:0.8821 V
  • STD:0.00083666
  • SEM:0.000374166

The purpose of this part of the experiments was to prove 2 things.


Experiment #2 Determination of h.

Results. Image:Plank's Constant Part 2.xls

Actual Plank constant:(4.13)E-15 eV*s

Measured h:(3.72±0.16)E-15 eV*s

Percent Error:9.92%

Actual work constant:1.36(8) eV

Measured W0=(1.66±0.01)V

Percent Error:22.05%

Aknowledgments

I used Ariannas Excel analysis to guide me through my analysis.


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