# Planck's Constant Summary

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## Summary

This lab is an investigation into the energy levels of electrons emitted in the photoelectric effect and the relationship between these energy levels and the frequency and intensity of the light source. This experiment uses a mercury vapor light source and an h/e Apparatus consisting of a vacuum tube wth a cathode emitter with a low work function and an anode receptor which develop a potential difference as electrons build up on the anode. When the stopping potential of the electrons is reached, the voltage difference, which can be read with a voltmeter, is stabilized and can be correlated to the kinetic energy of the electrons.
The relationships between the stopping potentials and the frequencies and intensities of the incident light are then analyzed with respect to both classical and quantum theories of light.
Planck's constant can be found through the equation:
E = h * frequency = KE(max) + Wo which can be rewritten in the form V(stopping) = h/e * f + Wo/e ,
the equation of a line with slope equal to h/e. Multiplying by the value for e, one may calculate the value of h, Planck's constant.

I plotted the average stopping potentials for each frequency versus frequencies and found:

Slope = 4.306 x 10^-15
Standard Error of the slope = +/-0.04597
y-intercept = 1.382 (which represents the work function of the surface material of the cathode)

Comparing this slope to the accepted value of 4.135 x 10^-15 eVs for Planck's constant, from Wikipedia Wikipedia, gives a percent error of:

(4.306 - 4.135)/4.135 = 4.1% error