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