midterm_2005s

# midterm_2005s - PHYSICS DEPARTMENT PRINCETON UNIVERSITY...

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Unformatted text preview: PHYSICS DEPARTMENT, PRINCETON UNIVERSITY PHYSICS 301 MIDTERM EXAMINATION October 26, 2005, 10:00–10:50 am, Jadwin A06 SOLUTIONS This exam contains two problems. Work both problems. The problems count equally although one might be harder than the other. Do all the work you want graded in the separate exam books. Write legibly. If I can’t read it, it doesn’t count! Put your name on all exam books that you hand in. (Only one should be necessary!!!) On the first exam book, rewrite and sign the honor pledge: I pledge my honor that I have not violated the Honor Code during this examination. Copyright c circlecopyrt 2005, Princeton University Physics Department, Edward J. Groth Physics 301 Midterm Exam Solutions 26-Oct-2005 Page 2 1. Consider atomic hydrogen in equilibrium at temperature τ . The temperature is low enough that the electron is in its ground state as far as its orbital motion is concerned. Be- cause the proton (the nucleus of the hydrogen atom) and electron each have spin 1 / 2, there are four possible states. There are very weak interactions (called hyperfine interactions) between the magnetic dipole moments of the proton and the electron. This produces an energy difference between the singlet and triplet states. This is called hyperfine splitting. The singlet state occurs when the proton and electron spins anti-align to form a spin 0 atom. The three triplet states occur when the proton and electron spins are aligned forming a spin 1 atom. Our model is a four state system with one state (the singlet) with energy 0 and the other three (the triplet states) with energy ǫ > 0....
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midterm_2005s - PHYSICS DEPARTMENT PRINCETON UNIVERSITY...

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