Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
Question
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Chapter 7, Problem 29E

(a)

To determine

Initial and final energy levels for third line in Paschen series

(b)

To determine

The wavelength of the line

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Whether the energy gap for a system decreases, is constant, or increases as the initial quantum number for the transition increases can be determined by calculating the second derivative of the energy level expression with respect to the quantum number. Calculate the second derivative with respect to the quantum number of the energy level expression for a linear rotor, EJ = hBJ(J+1) and also for the harmonic oscillator, Ev = hυ\upsilonυ(v+1/2).
Elaborate the importance of Angular momentum in Quantum Mechanics. Prove that the component of angular momentum obey the following commutation relation given in the image attached
Explain the energy level splitting of the Zeeman effect.

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