Let’s model a hydrogen atom as a single proton fixed in space with a single electron in a circular orbit at a radius of R=55×10-12 meters. Treat the circling electron as a current loop, and calculate the change in potential energy for that loop when a B=0.33 T external magnetic field goes from being aligned with the magnetic moment of the loop to being anti-aligned. (See figure.) (Note that this “classical approach” is not a good representation of what actually happens when a hydrogen atom interacts with a magnetic field.)
Some of these constants might be useful: me = 9.11 x 10-31 kg, mp = 1.67 x 10-27 kg, qp = 1.6 x 10-19 C, qe = -1.6 x 10-19 C.
Here are some steps you might take to work through this problem:
- What is the “current” for a single orbiting charge? Use the charge divided by the orbital period to get that current.
- Let the electrical force between the proton and the electron supply the centripetal force required to keep the electron in orbit, and solve for the angular frequency of the electron’s orbit. You may ignore contribution to the centripetal force provided by the external magnetic field. (Feel free to calculate it if you have time, it’s very small.)
- Calculate the magnetic moment for the current loop represented by the orbiting electron.
- Calculate the change in potential energy as the external magnetic field goes from being aligned with the magnetic moment to being anti-aligned.
your answer as a positive number in micro-electron-volts to at least two significant figures.
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