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AMO Exams - Quiz 1 1 Assume that the nucleus of the proton...

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Quiz 1. 1. Assume that the nucleus of the proton is a sphere of uniformly distributed charge. Take the radius of the sphere to be 1 fm=10 -13 cm. We will consider the ground state of atomic hydrogen and the ground state of the muonic hydrogen where the electron has been replaced by muon (mass of muon is 206 times larger than the electron). (i) Explain why the probability of finding the muon inside the nucleus is much larger. (ii) Calculate the probability of finding the electron and the muon, respectively, inside the nucleus. ( You can estimate the answer. If not, tell me how you will do the calculation.) 2. Use the Bohr model of atomic hydrogen to calculate the orbiting period of an electron in the excited state with principal quantum number n. What is the orbiting period for n=1, express your answer in femtoseconds. What is the period for n=25, 100, respectively? 3. Evaluate the spin-orbit interaction of the 3d state of atomic hydrogen. Consider the mass of the proton to be infinite. Express everything in your derivation in atomic units, but express the final answers in units of cm -1 . Hints: radial wavefunction, p159; some expectation values of radial wavefunctions, p.165. 4. High precision spectroscopy can be used to measure the radius of the nucleus. In the Oct 1, 2004 issue of Phys. Rev. Lett. 93, 142503 (2004), it was reported that the size of the so-called halo nucleus 6 He has been determined. The experimentalists measured the energy separation between two levels of an atom consisting of 6 He, as compared to one made of the normal 4 He nucleus. The nuclear spins of both nuclei are zero.
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