College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 28, Problem 31P

(a)

To determine

The number of distinct quantum state for n=1 energy level.

(b)

To determine

The number of distinct quantum state for n=2 energy level.

(c)

To determine

The number of distinct quantum state for n=3 energy level.

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An electron is in a hydrogen atom with n = 2 and ℓ = 1. (a) Find all the possible angles between the orbital angular momentum vector and the z-axis. (b) Suppose the atom absorbs a photon and rises from the n = 2 and ℓ = 1 state to the n = 3 state. Using conversation of angular momentum, what are the possible values of the final value of ℓ in the n = 3 state?
Which of the following is a permissable set of quantum numbers for an electron in a hydrogen atom? The atom may be in an excited state (ie. the electron need not be in its ground state). a) n = 6, l = -5, ml = +4, ms = +1/2 b) n = 4, l = -2, ml = +2, ms = -1/2 c) n = 2, l = 2, ml = +1, ms = -1/2 d) n = 5, l = 1, ml = -1, ms = +1/2 e) n = 3, l = 2, ml = -2, ms = -1
Angular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², 1 = 0,1,2,..., n-1 Lz = m₂ħ, m₁ = 0, ±1, ±2,..., ±l 3 S² = s(s+1)h² = h², 4 Consider an excited electron (n > 1) on an H-atom. Sz = msh 1 =+=ħ Show that the minimum angle that the I can have with the z-axis is given by n-1 n L.min = cos Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/V
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