(1) In the Bohr model of the hydrogen atom, the electron moves in a circular orbit of radius 0.5 x 10^{-10} m (0.5 angstroms) around the nucleus, which is a proton. Let's calculate some numbers! (a) Using laws named after Newton and Coulomb, find the speed of the electron. (b) Calculate the electric current, in amperes, of the electron moving in the circular orbit. (c) Calculate the dipole moment of the current loop of the electron. (d) Calculate the magnitude of the magnetic field at the center of the loop, i.e. the location of the proton. (e) The proton has an intrinsic magnetic dipole moment of 1.4 x 10^{-26} J/T. Calculate the difference in energy between the case when the proton is aligned and when it is anti-aligned with the magnetic field. Express your answer in electron-volts. (f) Calculate the wavelength of EM radiation for a photon of such energy using the quantum physics formula E = hc/?, where h is Planck's Constant, which you can look up. What classification of EM radiation is it? Refer to Fig. 33-1 in HRW.
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