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Planck's Constant (Photoelectric Effect)
Introduction & Safety
For this lab, we will be measuring a value for Planck's constant (h) by relating it to photoelectric effects caused by a Mercury lamp's light incident upon a cathode. There a few safety concerns that we will need to be careful about. These are high voltage, hot Mercury tube, and risk of breaking the tube or lens/grating. Most of these hazards have already been dealt with in previous labs (see Balmer Series) so we were already prepared for them. The only other important thing to note as far as safety is, as Aram pointed out, that we do not want to allow too strong of an intensity of light into our h/e apparatus because it could be damaging. To account for this, we will make sure to attach a filter which will simply decrease the intensity of light entering the apparatus.
Setup & Equipment
The lab was setup already, but we will still supply a brief description. We have a Mercury light source outfitted with a converging lens and diffraction grating pointed towards a "h/e" apparatus. This h/e apparatus is just a small circuit contained in a box. This circuit is basically just a piece of metal (the "cathode") which will receive photons from the Mercury lamp connected in series to a battery and an output (and ground). The battery is there so that we will have a voltage source that we can vary to measure the stopping potential from the output. The ground just resets the circuit so that the potential is zero again just before the cathode.
Before really getting started, we had to make sure our battery in the h/e apparatus still had enough voltage, so we connected the multimeter in parallel with the "Battery Test" connectors on the apparatus. We know, from the manual and from speaking with Aram, that the apparatus has two 9-volt batteries inside, giving a maximum potential of 18V if the batteries were new. The apparatus shows the minimum values, indicating ±6V which gives us a minimum of 12V that could be read through our multimeter. We actually measured our maximum potential to be
which is between the maximum possible (i.e. new batteries) and minimum possible (i.e. old batteries, not enough to stop photon energy) potentials.
Now that we know that we have good enough batteries to perform the experiment, we can start really setting things up. We begin by connecting our multimeter to the output connections on our h/e apparatus. This will display the exact stopping potential for the incident light. Next, we adjusted the distance between the light source and the lens/grating assembly, which slides on a pair of rods, until the light from the source was focused at the distance of the white reflective plate just in front of the apparatus input. We then rotated the apparatus until the focused light was centered (and focused) on the photodiode behind the light shield and reflective plate. After discharging the circuit to eliminate ambient voltage, we are ready to begin with the real procedure.
Experiment 1 consists of measurements that prove that the quantum theory of light is true and that the classical model for energy in light (which relates to intensity instead of frequency) is wrong.
The classical theory of light states that
which asserts that the stopping potential (and thus the kinetic energy of the photons) is proportional to the intensity of the incident light.
The quantum theory of light, however, states that
which asserts that the stopping potential is related directly to the frequency of the light. The W0 term indicates the work function of the metal that the light is incident upon.
Therefore, to show that classical thought is incorrect, all we need to do is show that the stopping potential is in fact proportional to the frequency, not the intensity, of the incident light. We do expect, however, the intensity of the light to affect certain things (like current, for example) so we will measure the "recharge time" which is the time for the potential to rise back up to the true potential after clearing out the energy in the circuit.
The following are tables for a few given colors and their corresponding frequencies emitted by Mercury that show our measurements for the stopping potentials with relation to recharge time and relative intensity.
For the second part of this lab, we will measure the value for Planck's constant, h, by using the conclusion from Experiment 1. We will use the same relation above for the stopping potential to determine this constant, since it is simply the proportionality constant for the transition from kinetic energy to frequency.
In order to get good enough data to get h within any kind of uncertainty, we need to take many data sets. Therefore, we will record data for all colors. Also, we will want to record data for both the first and second order maxima.
Analysis & Conclusions
For analysis, we will first plot our data. For Experiment 1, we will plot the relative intensity percentage with both the stopping potentials and the recharge time for all the colors we gathered data for. This will not be examined closely, but will give us an idea of the trends these values form. For Experiment 2, we will plot the stopping potentials for all colors, both first and second order, vs the frequencies (dictated by the colors). We will then use the equation relating stopping potential to frequency and Planck's Constant (h), as stated above, to determine a value for Planck's Constant.
This value is embedded in the slope for the extracted line (using Excel's LINEST aka Least Squares Fitting) and is related directly to the known value for the charge of an electron. We will also be able to extract what the value of our work function is because it is just related directly to the y-intercept for our stopping potential function (again with an electron charge factor).