{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–2. Sign up to view the full content.

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We will consider the ground state of atomic hydrogen and the ground state of the muonic hydrogen where the electron has been replaced by muon (mass of muon is 206 times larger than the electron).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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern