Question

PLEASE HELP WITH THESE THREE QUESTIONS

What is the orbital frequency (in Hz) of the electron as it orbits about the nucleus in the n = 100006 state of the Hydrogen atom? You can obtain this from the Bohr Model of the Atom by using the equations for the radius of the orbit and the speed of the electron. Since the orbital frequency is the number of revolutions per second that the electron undergoes as it orbits, you can determine this by finding the distance that the electron travels in one second (obtained from the speed of the electron as it orbits) and dividing this by the circumference of the electron's orbit (obtained by the radius of the orbit).

What is the photon frequency (in Hz) for a transition between the n = 100006 state and the n = 100005 state in a Hydrogen atom? To find the photon frequency, calculate the energy of the photon that is emitted during a transition between these two energy levels (use the Bohr Model of the Hydrogen Atom) and then calculate the photon frequency using the equation for the energy of a photon (from the Quantum Theory of Light).

In Classical Physics, the orbital frequency of the electron should equal the frequency of the emitted electromagnetic wave (i.e., the photon frequency), because the orbital frequency tells you how quickly the electron is vibrating back and forth. In Quantum Mechanics, the energy of the transition between allowed energy levels determines the emitted photon frequency. If you treat the photon frequency as the accepted value, what is the percent error (in %) between the orbital frequency and the photon frequency for n = 100006? Do these results agree with one another? According to Bohr's Correspondence Principle, the predictions of Quantum Mechanics should agree with the predictions of Classical Physics when applied to sizes where Classical Physics is known to work --- that is, for LARGE quantum numbers. Do the results for n = 7 and n = 100006 seem to obey the predictions of Bohr's Correspondence Principle
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Answer 1