1 \begin{problem*}{28.57} % photoelectric effect
2 The following table shows data obtained in a photoelectric
3 experiment. \Part{a} Using these data, make a graph similar to Active
4 Figure 28.9 that plots as a straight line. From the graph,
5 determine \Part{b} an experimental value for Planck's constant (in
6 joule-seconds) and \Part{c} the work function (in electron volts) for
7 the surface. (Two significant figures for each answer are
11 Wavelength (nm) & Maximum Kinetic Energy of Photoelectrons (eV) \\
18 \end{problem*} % problem 28.57
22 We can convert the wavelengths to frequencies and graph them
25 $\lambda$ (nm) & $f=c/\lambda$ (THz) \\
34 size(8cm, 5cm, IgnoreAspect);
41 real[] x = {588, 505, 445, 399}; // nm
42 real[] y = {0.67, 0.98, 1.35, 1.63}; // eV
44 // convert wavelength in nm to freq in THz
46 for (i=0; i<x.length; ++i) {
50 linefit L=leastsquares(x, y);
51 write("work function ", L.b);
59 draw(graph(fit, fmin, fmax), red);
60 draw(graph(x, y), p=invisible, marker=marker(scale(1pt)*unitcircle, blue));
62 pen thin=linewidth(0.5*linewidth())+grey;
63 xaxis("$f$ (THz)",BottomTop,
64 LeftTicks(begin=false,end=false,extend=true,ptick=thin));
65 yaxis("$K_{max}$ (V)",LeftRight,
66 RightTicks(begin=false,end=false,extend=true,ptick=thin));
70 The least-squares fit yields parameters \Part{c}
71 $\phi=\ans{1.4\U{eV}}$ and $h/e = 4.04\U{mV/THz}$. So \Part{b}
72 $h=\ans{6.5\E{-34}\U{J$\cdot$s}}$.