Problem 3
For 11.20b, a plot (created in Maple) of velocity of electron vs possible incident wavelengths of light.  The plot must be clearly labeled and all salient features must be clearly explained/dicussed -- be sure to explain what this plot "says" and why it "says" that.
We will be using equation 11.12 to make this graph.  Because we are making a plot of kinetic energy vs frequency, we know that in terms of x,y, y will be the kinetic energy which is directly proportional to the velocity of the emitted electron, and x will be frequency, which is inversely proportional to the wavelength.  We know this because in titles it is always Y vs X.  To start we need to rearrange the equation and put everything in terms of y (kinetic energy).
> eqn1112:=(1/2)*m*v^2=h*f-p;
aada
Another way to express this equation would be...                KE= h f - p
Variables
m = Mass of Electron
v = Velocity of Electron
h = Planck's constant
f = frequency
p = work function
l = wavelength
c= Speed of Light

Units
m = kg
v = m/s
h = J s
f = 1/s
p = J
l = ma
We need to set the variables as their constants.
> h:=6.62608*10^(-34);
a
> m:=9.10938*10^(-31);
a
> c:=2.99792458*10^8;
a
The binding energy was found in the previous problem.
> p:=0.1670622430e-15;
a
We know the values of h and p, so plugging in, we get.
> KE:=h*f-p;
a

> KE;
a
We have the kinetic energy of the electron in slope intercept form, so we can plot this.
> plot(KE,f=0..1e17.8,y=0..1e-16.5);
a
We can find the x-intercept by letting KE equal 0, then solving for the frequency.
> KE:=0;
a
> f=(KE+p)/h;
a
The x-intercept is 2.52 x 1017 Hz. 
Slope intercept form is y = mx + b.  Our y is the kinetic energy of the electron, our x is the frequency of the photon, m is Planck's constant, and b is the work function or the binding energy function.  The x-intercept is the lowest frequency at which a photon can collide with the metal and possess enough energy to cause the metal to emit an electron.  The electron will have a kinetic energy equal to the difference between the energy of the photon and work function.

 

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