Measurement of Planck’s constant, h - Astronomybelz/phys3719/presentations/peterson.pdfPlanck’s...
Transcript of Measurement of Planck’s constant, h - Astronomybelz/phys3719/presentations/peterson.pdfPlanck’s...
Measurement of Planck’s constant, h
Eric Peterson
PHYS 3719
4/6/11
[1]
Planck’s Constant
• Describes the size of quanta [2]
• Most prevalent constant along with c
• De Broglie Wavelength
• Uncertainty Principle
• Schrodinger Equation
• Currently accepted value: 6.62606896(33)x10-34 J·s [3]
• Experimentally measured value: (5.01±.03)x10-34 J·s
Outline
• Background
• Method: Photoelectric effect
• Data and Analysis
• Discussion of results
• Conclusion
Determination of h
• Planck- Black Body Radiation
– 6.55x10-34 J·s [2]
• Einstein- Photoelectric Effect, Theory [4]
• Millikan- Photoelectric Effect, Experimental
– 6.57x10-34 J·s [5]
• NIST- Moving Coil Watt Balance
– 6.626068910(88)x10-34 J·s [3]
[6]
Photoelectric Effect
• Why Photoelectric?
– Simple Physics
– Precise
– Classical vs. Quantum
The Physics
• Light shines on metal, ejecting electrons
• Model: E=hν
T=hν-φ
T= ½mv2=qV
qV=hν-φ
[7]
Method• Light shines through a series of
lenses to focus and increase intensity
• Light passes through monochromator
• “Monochromatic” light shines on photocell (cathode) releasing electrons
• Electrons are released and travel across potential to anode and current is measured
• Retarding voltage is set up to stop flow of electrons (zero current)
• qV =Tmax
Lamp
Series of Lenses
Monochromator
Photocell:Anode
Cathode
Retarding Voltage
Current Meter
A
Determine “zero current”
• Measure voltage at which current goes to zero
• Issue: What is “zero current”?
• Plan: Measure voltage with several different cutoffs
Data and Results
• Plot qV vs. Frequency
• Select most linear region by χ² test
Linearization of Data
• Perform a linear least squares fit to determine slope
• h= (5.01±.03)x10-34 J·s
Discussion
• Good agreement with model: χ²red=.93, r=.9999
• Only one measurement taken, so error in slope estimated from linear fit
• Residuals show random error is understood
• Largest source of error?
Improvements
• Measure voltages above and below zero current
– Interpolation of zero
• Measure “dark current”
Conclusion
• Photoelectric effect is a good method to determine h
• Measured value: (5.01±.03)x10-34 J·s
• Suggested improvements can help reduce systematic error
• Although percent error is high, data uphold Einstein’s theory: E=hν
• Experiment shows wave-particle duality of light
[8]
References
[1] http://www.siddeutsch.org/essay15.html[2] “Planck’s Constant”, http://en.wikipedia.org/wiki/Planck_constant[3] Williams, E. et al. “Accurate Measurement of the Planck Constant”.
Physical Review Letters, Volume 81, Issue 12. http://link.aps.org/doi/10.1103/PhysRevLett.81.2404
[4] “Photoelectric Effect”, http://en.wikipedia.org/wiki/Photoelectric_effect
[5] Millikan, R. “A Direct Photoelectric Determination of Planck’s ‘h’”. Physical Review, Volume 7, Issue 3. http://link.aps.org/doi/10.1103/PhysRev.7.355
[6] http://en.wikipedia.org/wiki/Ultraviolet_catastrophe[7] http://www.enotes.com/topic/Photoelectric_effect[8] https://www.llnl.gov/str/June05/Aufderheide.html