Treatise VWaves on a Spring + The Photoelectric Effect

Jahrme Risner

Section2Photoelectric Effect

Subsection2.1Background

In 1887 Heinrich Hertz observed that light striking a metal surface may release electrons. Philipp Lenard later showed that the emitted electrons have a maximum kinetic energy that depends on the wavelength but not the intensity of the light used. In 1905 Einstein correctly explained the photoelectric effect by invoking Planck's quantum hypothesis. According to Einstein, a photon of energy \(hc\lambda^{-1}\) knocks an electron from the target, giving the electron a kinetic energy \(hc\lambda^{-1}-W\), where \(W\) is called the work function, the minimum amount of energy needed to release one electron from that particular metal.

Subsection2.2Experimental Setup

We will measure the kinetic energy of the electrons by measuring the electric potential \(V_0\), called the stopping potential (measured in volts, symbol V), required to stop the most energetic electrons released. You do that by adjusting the potential on your box until the electron current reads zero. Kinetic energy \(K\) is related to stopping potential by \(K=eV_0\), where \(e\) is the electron's charge. The units for kinetic energy are electron volts (eV). If we measure say \(V_0=1.5\) V, then the electron's kinetic energy was \(1.5\) eV.

We can select a single wavelength by using a known light source, which produces a spectrum containing just a few visible wavelengths, and a filter that allows light of only a single wavelength to pass.

Using this, we begin by calibrating the box containing the photo-tube so that there is no current when the aperture is covered. From there, we insert the correct light filter and point the light into the box. We then adjust the voltage so as to get a current of \(0\); this is our \(eV_0\) for the current light's \(\lambda\). It should be noted, though, that when using yellow light there can be some difficulty in getting an accurate measurement.

The maximum kinetic energy of an emitted electron is \(K=eV_0\). According to Einstein's theory, this maximum kinetic energy is related to the wavelength of light and the metal's work function according to \(eV_0=hc\lambda^{-1}-W.\) We would like to measure Planck's constant \(h\), and in doing so verify the quantum (photon) nature of light. In this experiment it's easier to measure \(hc\), which effectively measures Planck's constant, because the speed of light \(c\) is well known. In our data, we measured the stopping potential \(V_0\) for several different wavelengths \(\lambda\). We have plotted \(eV_0\) (in units of eV) versus \(\lambda^{-1}\) (in units of nm) in Figure 2.2; the result is a straight line with a slope \(hc\). The accepted result is \(hc = 1240\) eV nm. We are within a factor of two of this result; as such, we can say we've measured the smallest constant in nature, Planck's constant.

As a bonus, the intercept of our graph gives us the metal's work function, in units of eV. Most metals have a work function between \(0\) and \(5\) eV and ours falls into that range at \(0.97\).

Historical Significance

This experiment established the quantum notion of light whereby light (as well as matter, though that is another issue) exhibits both particulate and wavelike properties, suggesting that traditional mechanics can not always account for our physics. Additionally, the experiment was revolutionary as previously it had been believed that the amount of energy conveyed by light was dictated by the intensity of the light, in other words how bright it was. However, as can be seen in this experiment, it is the wavelength of light that really determines the energy conveyed when attempting to liberate electrons.