Planck’s Constant and the Photoelectric Effect

Lulu Liu

Partner: Pablo Solis

Junior Lab 8.13 Preparatory Lab

September 25th, 2007

What is the Photoelectric Effect?

Image from Wikipedia Commons

Incident radiation

Work Function W0

– closely related to F

Eabsorbed < W0

) electron still bound

Eabsorbed > W0

) electron free Heinrich Hertz

Predictions

Classically, wave mechanics: Eradiation I E02

Continual Absorption;

Eradiation 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

Kmax = h – W0

Graphic from TeachNet.ie

How do we measure Kmax?

Predicted Behavior

Retarding Voltage Vr

eVr = Kmax when I ! 0

) Vs = Vr = Kmax

/ e

The Experiment

Cathode: W0 = 2.3 eV

Anode: Wa = 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 (Vs)

• Vs 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 Vs

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 (Vs,I0) – baseline current.

Use three points farthest from Vs. Reasonable chi-squared.

Results of the Linear Fit Method

In eV:

Kmax = h – W0

h = 9.4 £ 10-16

§ 4.8 £ 10-16 eV ¢ s

W0 = 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 (Vs) 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 £ 10-16 § 4.8 £ 10-16 eV¢ s

Deviation point method: h = 2.9 £ 10-15 § 7.7 £ 10-16 eV ¢ s

(systematic error determined by square-root of variance in the values of h)

h = 1.92 £ 10-15 § 1.08 £ 10-15 eV ¢ s

actual: h = 4.135 £ 10-15 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 Kmax 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) £ 10-15 eV ¢ s

Calculated Actual

h = 4.135 £ 10-15 eVs

CPD – contact potential difference

V = V’ – (A - C)

Vr = (h/e) - A

Cathode material deposition on anode - results in erroneous work functions.

Zero-Intercept Method