From b606cc565f91c5ba2176893957a1cd7e86d728bc Mon Sep 17 00:00:00 2001
From: "Eugeniy E. Mikhailov" <evgmik@gmail.com>
Date: Wed, 28 Aug 2019 16:37:37 -0400
Subject: Synchronized manual with one of Justin

Updated source was located at
located at https://bitbucket.org/jrsteven/phys251_manual/src/master/
---
 pe-effect.tex | 102 ++++++++++++++++++++++------------------------------------
 1 file changed, 38 insertions(+), 64 deletions(-)

(limited to 'pe-effect.tex')

diff --git a/pe-effect.tex b/pe-effect.tex
index 976511a..aaf1adc 100644
--- a/pe-effect.tex
+++ b/pe-effect.tex
@@ -138,11 +138,7 @@ the $h/e$ apparatus.
 \end{itemize}
 
 \item Go back to the original spectral line.
-\item Place the variable transmission filter in front of the white
-	reflective mask (and over the colored filter, if one is used) so
-	that the light passes through the section marked 100\% and reaches
-	the photodiode. Record the DVM voltage reading and  time to
-	recharge after the discharge button has been pressed and released.
+\item Place the variable transmission filter in front of the white reflective mask (and over the colored filter, if one is used) so that the light passes through the section marked 100\% and reaches the photodiode. Record the DVM voltage reading and time to recharge after the discharge button has been pressed and released.
 \item Do the above measurements for all sections of the variable transmission filter. 
 
 \end{enumerate}
@@ -153,46 +149,45 @@ the $h/e$ apparatus.
 The mercury lamp visible diffraction spectrum.}
 \end{figure}
 
-\section*{Part B: The dependence of the stopping potential on the frequency
-    of light}
+\section*{Part B: The dependence of the stopping potential on the frequency of light}
+
+In this section you'll measure the stopping power for the five different emission lines of Mercury to demonstrate that the stopping power depends on, and is a measurement of, the wavelength (and frequency).  Your measurements will consist of the stopping power for each of the five Mercury lines, measured for both first and second orders.  This is a total of 10 data points.  You'll then analyze the data by fitting stopping power vs frequency to extract Planck's constant and the work function. That procedure is described in more detail in the next section. 
+
+There is a particular issue with the yellow and green lines that, if left unaddressed, can corrupt your measurements. The procedure below walks you through the measurements of those two lines lines, highlighting a few a few places that systematic problems can creep in if we are not careful.  In particular, you will be using yellow and green filters to mitigate one source of systematic bias.  
+
 \begin{enumerate}
-\item You can easily see the five brightest colors in the mercury light spectrum. Adjust the $h/e$ apparatus so that the 1st order yellow colored band falls upon the opening of the mask of the photodiode. Take a quick measurement with the lights on and no yellow filter and record the DVM voltage. Do the same for the green line and one of the blue ones. 
 
-\item Repeat the measurements with the lights out and record them (this will require coordinating with other groups and the instructor).  Are the two sets of measurements the same?  Form a hypothesis for why or why not.
-\item Now, with the lights on, repeat the yellow and green measurements with the yellow and green filters attached to the h/e detector. What do you see now?  Can you explain it? (Hint: hold one of the filters close to the diffraction grating and look at the screen).
-\item Repeat the process for each color using the second order lines.  Be sure to use the green and yellow filters when you are using the green and yellow spectral lines.
+
+\item Adjust the $h/e$ apparatus so that the 1st order yellow colored band falls upon the opening of the mask of the photodiode. Take a quick measurement with the lights on and record the DVM voltage. Do the same for the green and blue lines. 
+
+\item Now, with the lights still on, repeat the yellow and green measurements with the yellow and green filters attached to the h/e detector. What do you see now?  In order to explain your observations try holding the filters just in front of the diffraction grating and look at the pattern on the screen.
+
+\item Now turn the lights off.  This will require coordinating with other groups and the instructor. Repeat the measurements with and without the filters. Are the two sets of measurements the same?  Form a hypothesis for why or why not.
+
+\item Now, you need to decide on the best procedure for collecting the data. Lights on or lights off? Filters or no filters? Discuss amongst your group and with the instructor or TA.   You will need to measure both the first and second order lines. This is all five colors, for a total of 10 data points.
+
+Note: When collecting the data in the steps above, be sure to estimate uncertainties on the stopping power. These come in part from the digital voltmeter, but also from the repeatability of your measurements, how well lines are centered on the slit (perhaps off-center could be better?) and so on.
 
 \end{enumerate}
 
 \section*{Analysis}
 \section*{Classical vs. Quantum model of light}
 \begin{enumerate}
-\item Describe the effect that passing different amounts of the same
-colored light through the Variable Transmission Filter has on the stopping
-potential and thus the maximum energy of the photoelectrons, as well as the
-charging time after pressing the discharge button.
-\item Describe the effect that different colors of light had on the stopping
-potential and thus the maximum energy of the photoelectrons.
-\item Defend whether this experiment supports a classical wave or a
-quantum model of light based on your lab results.
+\item Describe the effect that passing different amounts of the same colored light through the Variable Transmission Filter has on the stopping potential and thus the maximum energy of the photoelectrons, as well as the charging time after pressing the discharge button.
+
+\item Describe the effect that different colors of light had on the stopping potential and thus the maximum energy of the photoelectrons.
+
+\item Defend whether this experiment supports a classical wave or a quantum model of light based on your lab results.
 \end{enumerate}
-Read the theory of the detector operation in the Appendix, and explain why
-there is a slight drop in the measured stopping potential as the light
-intensity is reduced. \\{\bf NOTE:} While the impedance of the unity gain
-amplifier is very high ($10^{13}~\Omega$), it is not infinite and some charge
-leaks off. 
+
+Read the theory of the detector operation in the Appendix, and explain why there is a slight drop in the measured stopping potential as the light intensity is reduced. 
 
 \section*{The relationship between Energy, Wavelength and Frequency}
 
 \begin{enumerate}
-\item
-Use  the table in Fig.~\ref{fig:mercury_spectrum} to find the exact frequencies and wavelengths of the spectral lines you used and plot the measured stopping potential values versus light frequency for measurements of the first and second order lines (can be on same graph).
+\item Use the table in Fig.~\ref{fig:mercury_spectrum} to find the exact frequencies and wavelengths of the spectral lines you used and plot the measured stopping potential values versus light frequency for measurements of the first and second order lines.
 
-\item Fit the plots according to $eV_0 = h\nu-\phi$, extracting values for
-	slopes and intercepts. Find the average value for slope and its
-	uncertainty. From the slope, determine  $h$ counting
-	$e=1.6\cdot10^{-19}$~C. Do your measured values agree with the
-	accepted value of  $h=6.62606957(29) \times 10^{-34}$J$\cdot$s within experimental uncertainty?
+\item Fit your data according to $eV_0 = h\nu-\phi$, extracting values for the slope and intercept. {\it Note, this fitting step takes the measurement uncertainties on the stopping power and propagates them to the slope and intercept.} It's important to do this step with Igor, Matlab, or some other tool which can compute a $\chi^2$, minimize it with respect to the fit parameters, and then report the parameter uncertainties.  From the slope, determine  $h$ using $e=1.6\cdot10^{-19}$~C. Find the average value and uncertainty on the average. Does your value agree with the accepted value of  $h=6.62606957(29) \times 10^{-34}$J$\cdot$s within uncertainty?
 
 \item From the intercepts, find the average value and uncertainty of the work function $\phi$. Look up some values of work functions for typical metals. Is it likely that the detector material is a simple metal?
 
@@ -201,6 +196,7 @@ Use  the table in Fig.~\ref{fig:mercury_spectrum} to find the exact frequencies
 \section*{Appendix: Operation principle of the stopping potential detector}
 
 The schematic of the apparatus used to measure the stopping potential is shown in Fig.~\ref{pefig5}. Monochromatic light falls on the cathode plate of a vacuum photodiode tube that has a low work function $\phi$. Photoelectrons ejected from the cathode collect on the anode. The photodiode tube and its associated electronics have a small capacitance which becomes charged by the photoelectric current. When the potential on this capacitance reaches the stopping potential of the photoelectrons, the current decreases to zero, and the anode-to-cathode voltage stabilizes. This final voltage between the anode and cathode is therefore the stopping potential of the photoelectrons.
+
 \begin{figure}[h]
 \centering \includegraphics[width=0.7\linewidth]{./pdf_figs/pe_det}
 \caption{\label{pefig5} The electronic schematic diagram of the $h/e$
@@ -214,12 +210,13 @@ front panel of the apparatus. This high impedance, unity gain ($V_{out}/V_{in}
 = 1$) amplifier lets you measure the stopping potential with a digital
 voltmeter.
 
-Due to the ultra high input impedance, once the capacitor has been charged from
-the photodiode current, it takes a long time to discharge this potential through
-some leakage. Therefore a shorting switch labeled ``PUSH TO Zero'' enables the
-user to quickly bleed off the charge.
+Due to the ultra high input impedance, once the capacitor has been charged from the photodiode current, it takes a long time to discharge this potential through some leakage. Therefore a shorting switch labeled ``PUSH TO Zero'' enables the user to quickly bleed off the charge. While the impedance of the unity gain amplifier is very high ($10^{13}~\Omega$), it is not infinite and some charge gradually leaks off. This effect can bias the measured stopping power for low intensity light sources.
+
 \newpage
 \section*{Sample data tables:}
+
+\subsection*{Part A}
+
 {\large
 %\begin{tabular}{|p{27mm}|p{27mm}|p{27mm}|p{27mm}|}
 \begin{tabular}{|c|c|c|c|}
@@ -233,45 +230,22 @@ Approx. Charge Time \\
 &40&&\\ \hline
 &20&&\\ \hline
 \hline
- Color & \%Transmission & Stopping Potential &
-Approx. Charge Time \\
-\hline
-&100&&\\\hline
-&80&&\\ \hline
-&60&&\\ \hline
-&40&&\\ \hline
-&20&&\\ \hline
 \end{tabular}
 }
-\vskip .1in
-%
-%
-%{\large
-%\begin{tabular}{|p{27mm}|p{27mm}|}
-%\hline
-% Light Color  & Stopping Potential \\\hline
-%Yellow&\\\hline
-%Green&\\ \hline
-%Blue&\\ \hline
-%Violet&\\ \hline
-%Ultraviolet&\\ \hline
-%\end{tabular}
-%}
+
+\subsection*{Part B}
 
 {\large
 \begin{tabular}{|c|c|c|c|}
 \hline
- 1st Order Color&$\lambda$ (nm) &$\nu$  ($10^{14}Hz$) &
+Color&$\lambda$ (nm) &$\nu$  ($10^{14}Hz$) &
 Stopping Potential (V) \\
 \hline Yellow&&&\\\hline Green&&&\\ \hline Blue&&&\\ \hline Violet&&&\\
-\hline Ultraviolet&&&\\ \hline \hline
-2nd Order Color&$\lambda$ (nm) &$\nu$  ($10^{14}Hz$) &
-Stopping Potential (V) \\
-\hline Yellow&&&\\\hline Green&&&\\ \hline Blue&&&\\ \hline Violet&&&\\
-\hline Ultraviolet&&&\\ \hline \hline
-
+\hline Ultraviolet&&&\\ \hline 
 \end{tabular}
 }
 
+You'll either want different tables for different orders, or perhaps add additional stopping power columns to the one above.
+
 \end{document}
 
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