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Fall 07 Phys 143l HW 10 Solutions

Fall 07 Phys 143l HW 10 Solutions - Physics 143 Fall Term...

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P a g e | 1 3 Physics 143 Fall Term 2007 HOMEWORK 10 Due: November 20 Problem 1: (BFG Ch.9 Problem 21) Consider a hydrogen atom in a magnetic field. The quantum state splits by m , there are 2l൅1 energy levels: ሺright figureሻ There are 5 ൈ 3 ൌ 15 possible transitions. When we take into account that: ∆m ൌ െ1, 0, 1 All the red dashing lines are forbidden. The energy of each state is ሺBFG Equ. 9‐47ሻ E ൌ E eB԰ 2m m Therefore the transition energy is:ሺnൌ3, lൌ2 Æ nൌ2,lൌ1ሻ ∆E ൌ ሺE െ E ሻ െ eB԰ 2m ∆m And thus the frequency of the corresponding spectral line is: f ൌ ΔE h which indicates that transitions with same ∆m will result in the spectral line with same frequency in the spectrum. We can calculate the value of ∆m of each transition. There are 3 cases: 3 transitions with ∆m ൌ െ1; 3 transitions with ∆m ൌ 0; 3 transitions with ∆m ൌ 1.
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