Physics307L F08:People/Young/Young's Planks Constant

Brief summary
In this lab we used the photoelectric effect to charge a capacitor to it's maximum. Since the charging of a capacitor is defined by an exponential function we can assume that our our function for our rise times are exponential functions. Using multiple lines of a spectrum from a Helium light and changing intensities for each spectrum we can use the time constant which we will call τ. With this time constant and our closest guess to the max voltage we are going to predict the classic variable of Plank's constant.
 * notebook entry for Planck's Constant lab
 * lab manual.

Error Analysis
In this lab many assumptions were made that could result in error in our final analysis.


 * The Capacitor that we are using may not be described exactly by a single exponential function.
 * Since our Max Voltage readings should have been read at time=infinity to be perfect our max voltage and time readings are slightly lower than they should be.
 * The three blues lines were very close and seemed to intersect at some points. The blue line may have some confusing results due to human error.
 * Ambient light could have interfered with our readings.

In an attempt to look at the true shape of the rise time curve we attached an oscilloscope to the capacitor box. Often when the discharge button was released the voltage would shoot up and down in an unpredictable manner. While using the oscilloscope to map the rise time would be more accurate form of measuring planks constant our time restraints forces us to stick to our former method

Analysis
Starting with the formula relating our Voltage to Energy.
 * $$\ V = \ E - \ W\,$$,

and plugging in our relation between planks constant and Energy
 * $$E = h \nu \,$$

We have
 * $$\ V = h \nu - \ W\,$$,


 * Frequency can is a value that has units of 1/s which would be the value of our time constant τ. Knowing this we must find our values for τ and then we can make a plot of Vmax vs τ where the slope will be our planks constant value.

Finding τ

Find the time constant proved to be a very difficult task. At first I thought that I could use the same Vmax for all intensities that we measured in our lab. However, since the capacitor slowly looses charges to our volt meter we a not say that the Vmax for all intensities is the same. This is because our Capacitor looses charge at a slow rate due to our Voltmeter being attached. If the rate at which charge is being placed on the capacitor is decreased this makes it harder for us to reach our max Voltage. Therefore we have smaller Vmax's for lower intensities. After much effort I discovered this was a dead end. In order to find the time constant we would have to make assumptions about our apparatus that is not true at all. The Oscilloscope gave us the general shape of our rise time ,but with our limited time we decided to take another route to find the time constant.

If we could find the time constants they would have this shape.

Using Energy to find Planks Constant. r Using the above equations and the information gathered in Experiment two from our lab book we have a linear plot. Using matlabs polyfit function on frequency vs. Vmax I found the slope of our graph. The polyfit function output an error of 0.000 Causing me to believe that the error done by the analysis is negligible.

I found Planks constant to be....

h=4.293e-15

Comparison of accepted value of h with my value for h

%error= 103.8043%

Despite how close my constant looks to the accepted value there is still a large discrepancy. I attribute this error to the things discussed in the Error Analysis section.

To take this experiment further I would explore the use of the Oscilloscope more. I believe that the finding and analyzing the true function for rise time would be the most accurate way of calculating Planks constant.