# Two Features of the Photo-Electric Effect Essay

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The photo electric effect, which was first documented by Einstein in 1905, and posited that the energy of liberated electrons is linearly dependent on the frequency of incident photons. This paper investigates this relationship and measures Planck's constant ($4.36\pm 0.04\e{-21}$MeVs), and the work function of the photo diode ($-1.52\pm0.02$V). Another phenomena which is checked is the charging time of the stopping potential voltage. While there was some dependence between stopping voltage and intensity, this effect is mostly systematic. Both of these experiments provide evidence that the energy imparted by incident photons is dependent on the frequency, and the number of photo electrons is dependent on the number of…show more content…
This gives the following relationship: $$\label{eq:linearPE} V = \frac{h}{e}\nu - \frac{W_o}{e}$$ This allows the measurement of the stopping voltage as a function of frequency. Fixing the elementary charge ($e$) as a known, this allows for an experimental determination of Planck's constant ($h$) and the work function of the material ($W_o$). This paper examines two scenarios. The first is a fit to the data using (\ref{eq:linearPE}) to measure $h$ and $W_o$. The second scenario investigates the time dependence of the charge development as a function of intensity. \subsection{Theory} The photo-electric effect is explained in the following situation. Photons with an energy $h\nu$ are incident on a material which can be characterized by a work function $W_o$. This work function represents the amount of energy required to liberate an electron from the atom. The effect postulates a number of experimental results which are easily tested. One is that the work function $W_o$ is independent of the intensity of the incident photons. Here we define intensity as a number density rather than something which scales with the amplitude of the incident electromagnetic waves. This means that the energy of the ejected photons will be independent of the number of incident photons because each electron ejected will be related to the incident photon energy. Conversely, this predicts that the number of liberated