PS+5 - 6.28.) 4. Problem 6.21. 5. Problem 7.8. 6. Plot...

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Physics 113B, Fall 2011 Problem Set #5 (Due Tuesday, Nov. 22, 2011 in class) 1. The g-factor for the electron g e = 2.0023 and for the proton g p = 5.5857. Express the hyperfine energy gap ΔE hf for the hydrogen atom in terms of the ground state Bohr energy for hydrogen E 1 and the g factors g e and g p , the mass of the proton m p , and the speed of light c. 2. Express the fine structure correction in terms of the hyperfine energy gap ΔE hf and compare the two. 3. Calculate the hyperfine energy gap ΔE hf for a positronium using the reduced mass for calculating the Bohr radius. In a positronium, the proton is replaced by the a positron. A positron has the same mass as the electron but has the opposite charge. (See problem
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Unformatted text preview: 6.28.) 4. Problem 6.21. 5. Problem 7.8. 6. Plot numerically the function F(x) given in Eq. 7.51 and shown in Fig. 7.7. Find the value of x at the minimum of F(x), x = R/a where R is the internuclear distance in H 2 + molecular ion and a = 0.52917706 is the Bohr radius. Calculate the second derivative at the equilibrium position and obtain the ground state vibrational energy of H 2 + (/2). Compare the ground state vibrational energy to the depth of the well in F(x), i.e. the binding energy of H 2 + . How many vibrational levels are there in the well? (See problem 7.10.)...
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This note was uploaded on 12/13/2011 for the course PHYS 113B taught by Professor Staff during the Fall '11 term at UC Irvine.

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