6.3    THE EXPERIMENT AT HIGH VELOCITIES

The original Davisson-Germer experiment is valid only under the approximations of slow velocity electrons where Classical Physics apply. In this case the following assumptions are valid:

1) Kinetic Energy = E_k = ½ mv²

2) Electric Potential = potential difference measured by a voltmeter = V

Now we will consider the same experiment but at high velocities. Important considerations must be taken on the assumptions above.

First, the new theories predict the mass of the electrons to be constant under velocity variations then, even at high velocities, the classical formula for the Kinetic Energy remains valid:

E_k = ½ mv²                      (m is constant)

Second, with the new theories the second assumption is no longer valid for high energy electrons.

It must be considered that the new Electric Field proposed have the factor s that is velocity dependent:

E = sKq/r²

It is evident that the Electrical Potential (which by definition is equal to the work done by the Electric Force over a particle of unity charge) will be also velocity dependent and it seems very difficult to calculate. More important, it is no more equal to the measured voltage by a voltmeter. The potential measured by a voltmeter between the accelerator plates will serve only for slow electrons where Classical Physics can apply.

 This implies that the velocity gained in the accelerator of the apparatus will be different to that computed with the original formula.

A different method to obtain the velocity that will be used to verify the De Broglie formula should be considered.

One possibility to be suggested is the addition of an electric/magnetic velocity selector in the apparatus after the accelerating stage to determine more directly the velocity of the electrons. The velocity selector uses crossed electric and magnetic fields (the factor s cancels out) that produces opposite forces only on the electrons at a given precise velocity that will pass through a narrow slit. The electrons with other velocities are deviated and will not pass to the diffraction stage.