(adsbygoogle = window.adsbygoogle || []).push({}); Electrons are accelerated through a potential V into a cloud of cold atomic hydrogen. A series of plates with aligned holes select a beam of scattered electrons moving perpendicular to the plates. Immediately beyond the final plate, the electrons enter a uniform magnetic field B perpendicular to the beam; they curve and strike a piece of film mounted on the final plate. When the film is developed, a series of spots is observed. The distances between the hole and the two most distant spots are measured. Find the magnitude of B, of V, and the total number of spots on the film. Basically, an electron gun is shooting electrons into cold atomic hydrogen. Something happens, and electrons come out of the other side, passing through a velocity selector and then a uniform magnetic field.

The first part of the problem (not shown) required me to calculate the energy of an electron, which I derived as [tex]E_n = -\frac{2.18 x 10^{-18} J}{n^2}[/tex].

I know how to find the velocity of the electrons entering the cloud of cold atomic hydrogen: [tex]eV = \frac{mv_i^2}{2}[/tex]. I also know how to find the magnitude of the magnetic field: [tex]\frac{mv_f}{|q|R} = B[/tex]. What I don't know how to find is [itex]v_f[/itex].

I don't know what's going on in the cold atomic hydrogen. I figured that since the electrons are all entering with a uniform velocity, then they will all leave with the same velocity (might be different from the initial one, though) and hit the same place on the film after curving around. However, according to the problem, the electrons are "scattered" and hit different points on the film. This makes no sense to me - how can I calculate this scattering?

The closest I got to understanding what's going on was writing this:

[tex]\frac{mv_i^2}{2} -\frac{2.18 x 10^{-18} J}{n^2} = \frac{mv_{f1}^2}{2} - \frac{mv_{f2}^2}{2}[/tex]. But then I had no idea how to find [tex]v_{f2}[/tex] and [tex]v_{f1}[/tex].

In summary, here are my questions:

- What is going on in the cold atomic hydrogen?
- How can the electrons be "scattered"?
- What is leaving the cold atomic hydrogen?
- How can I calculate the final velocities of the electrons?

All of these questions are closely interrelated, so I just need a push in the right direction.

Thanks in advance.

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# Electrons being fired at cold atomic hydrogen

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