Planck's constant

Conversion: wavelength to frequency:

>	restart; with(plots):

Warning, the name changecoords has been redefined

>	f:=lambda->evalf(c/lambda);

>	c:=3*10^8;

>	f(550*10^(-9));

>	# Giga=10^9, Tera=10^12  We have 545 Terahertz

>

n:=1E-9;

>	WL:=[400*n,450*n,500*n,550*n,600*n,650*n];

>	FR:=map(f,WL);

>	Volts:=[1.35,1.05,0.86,0.68,0.50,0.305];

>	e:=1.6E-19;

>	PL1:=plot([seq([FR[j],Volts[j]],j=1..nops(FR))],style=point,symbolsize=20,symbol=box): display(PL1);

>	with(stats):

>	sol:=fit[leastsquare[[f,V]]]([FR,Volts]);

>	PL2:=plot(rhs(sol),f=FR[1]..FR[nops(FR)],color=blue,thickness=3): display(PL1,PL2);

>	coeff(rhs(sol),f)*e;

>	Planck:=6.6E-34*Js;

Why do we get a value that is too low by almost 20% ???

The straight-line fit looks actually quite good. If we repeat the measurements, we are likely to get results that will be consistent with the slope obtained from the 6 data points.

We are looking for a systematic deviation: are there physical reasons why the slope comes out to be too low?

One possible systematic effect: the reverse photoeffect.

For short wavelengths (high frequencies, blue colour) photons can knock out electrons from the post which will be collected at the mantle. At red to green colours this reverse photoeffect does not work, since the photon energy is not sufficient to remove electrons from the post (the work function for the post is higher than for the mantle).

This can have the effect of reducing the photovoltage measured for the blue colours.

If the last two data points were slightly higher, a more consistent line fit would emerge, and it would yield a bigger slope.

If one wants to understand systematic effects, one has to do more analysis.

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