Question

a muonic atom has an electron replaced by a particle called a muon, which is about 200 times more massive, but otherwise almost the same as an electron before you start the rest of this, you'll want to check what quantities for a bohr hydrogen atom depend on the electron mass. consider a muonic hydrogen atom in its ground state. ignore subtle effects like the reduced mass or any relaticistic considerations (even though the former should be relevant here). Remember that in a bound electrostatic system the kinetic energy is equal to the opposite of the total energy. Calculate:

a) The orbital frequency and the wavelength corresponding to classical electron-magnetic waves of this frequency

b) The frequency and wavelength of a photon with just enough energy to ionize the system

c) The de broglie wavelength and the de broglie frequency for the muon

d) Another relevant length scale is the so-called "compton wavelength" of the muon, which is the wavelength corresponding to the rest-energy of the particle assuming the speed of light. calculate the compton wavelength of the muon e) yet one more relevant length scale is the radius of this atom, a0(u). Taking this length as an uncertainty on where the muon might be found, what is the minimum uncertainty on momentum?

Answer 1