Planck’s Constant and the Photoelectric Effect Lulu Liu Partner: Pablo Solis Junior Lab 8.13 Preparatory Lab September 25 th, 2007

What is the Photoelectric Effect? Image from Wikipedia Commons Incident radiation Work Function W 0 – closely related to  F E absorbed < W 0 ) electron still bound E absorbed > W 0 ) electron free Heinrich Hertz

Predictions Classically, wave mechanics: E radiation  I  E 0 2 Continual Absorption; E radiation does not depend on What if light was a particle with discrete E? - E > W, electron absorbs E and is freed with kinetic energy E – W - E < W, electron re-emits E as a photon, stays bound.

Presentation Outline Predicted relationship between E and Experimental techniques – Set up and Parameters Current vs. retarding voltage data Analysis – Two Methods – Linear Fit Method Results and Error Conclusions and Summary

Hypothesis E = h is frequency h is Planck’s constant K max = h – W 0 Graphic from TeachNet.ie How do we measure K max ? Predicted Behavior Retarding Voltage V r eV r = K max when I ! 0 ) V s = V r = K max / e

The Experiment Cathode: W 0 = 2.3 eV Anode: W a = 5.7 eV

Photocurrent vs. Retarding Voltage – Raw Data (Example)

Normalized Current vs. Retarding Voltage Curves for All Wavelengths Normalization removes scaling by differences in intensity. Back currents Non-linear character near stopping voltage (V s ) V s has clear dependence on frequency Two methods of extrapolating cut-off voltage, difference estimates systematic error.

Linear Fit Method of Cut-off Voltage Determination Motivation: Using zero-crossings for V s determination compromised by back currents and non-linear behavior. Does behave linearly at low and high limits (discounting forward current saturation). Fit the low and high voltage data to separate linear regressions. Extrapolate intersection point (V s,I 0 ) – baseline current. Use three points farthest from V s. Reasonable chi-squared.

Results of the Linear Fit Method In eV: K max = h – W 0 h = 9.4 £ § 4.8 £ eV ¢ s W 0 = 0.07 § 0.30 eV

Error Contributions and Calculations for Linear Fit Method Two linear regressions y = mx + b with uncertainties on m,  m1 and  m2, and b,  b1 and  b2 contribute to the error in the X- coordinate of their intersection (V s ) as follows: Propagation of the experimentally determined random error.

Determination of Planck’s Constant Using Results from Both Methods Linear fit method: h = 9.4 £ § 4.8 £ eV¢ s Deviation point method: h = 2.9 £ § 7.7 £ eV ¢ s (systematic error determined by square-root of variance in the values of h) h = 1.92 £ § 1.08 £ eV ¢ s actual: h = £ eV ¢ s

Error Sources and Improvements for Future Trials Random error – cannot reduce but better characterization – More trials, more independent trials (reset equipment? time between trials?) Systematic error – V applied is not V overcome by free electrons – Back currents – more data points, extend measurements deeper into high and low voltage ends. – Brighter source – better resolution and less relative error. Items still to be explored – Explicit relation between intensity of light and K max of electrons

Conclusions Verification of hypothesis – observed light behave as a particle – confirmed linear relation between E and Two Analysis Methods – useful as estimate of systematic error – well-bounded the ambiguity of cut-off voltage h = (1.92 § 1.08) £ eV ¢ s CalculatedActual h = £ eVs

CPD – contact potential difference V = V’ – (  A -  C ) V r = (h/e) -  A Cathode material deposition on anode - results in erroneous work functions.

Zero-Intercept Method