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

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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 Å is the Bohr radius. Calculate the second derivative at the equilibrium position and obtain the ground state vibrational energy of H 2 + (ћω/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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