Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Question
Chapter 9, Problem 12P
(a)
To determine
The spectroscopic notation for
(b)
To determine
The possible states of electron which have
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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
Quantum Physics
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
Chapter 9 Solutions
Modern Physics
Ch. 9.2 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9 - Prob. 1QCh. 9 - Prob. 2QCh. 9 - Prob. 3QCh. 9 - Prob. 4QCh. 9 - Prob. 5QCh. 9 - Prob. 6QCh. 9 - Prob. 7QCh. 9 - Prob. 8Q
Ch. 9 - Prob. 9QCh. 9 - Prob. 11QCh. 9 - For a one-electron atom or ion, spinorbit coupling...Ch. 9 - Prob. 14QCh. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 4PCh. 9 - The force on a magnetic moment z in a nonuniform...Ch. 9 - Consider the original Stern–Gerlach experiment...Ch. 9 - Prob. 7PCh. 9 - Consider a right circular cylinder of radius R,...Ch. 9 - Prob. 9PCh. 9 - Prob. 10PCh. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Prob. 14PCh. 9 - Prob. 15PCh. 9 - Prob. 16PCh. 9 - Prob. 17PCh. 9 - Prob. 18PCh. 9 - Prob. 21PCh. 9 - Prob. 22PCh. 9 - Prob. 23PCh. 9 - Prob. 24PCh. 9 - Prob. 25P
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- H-atom. The wave function of one of the electrons in the 2p orbital is given by (ignoring spin) r 2,1,0 (1,0,0)= - 7 exp(-270) c ao 1 |32πα cose Where do is the Bohr radius. In the Bohr model, the radius of the electron orbit is given by m=2 = n²ao = 4ao. The probability that the electron can be found at some radius between r and r + dr is given by 2π P(r) dr = √2 = √ ₁²ª d$ S ² What is the expectation value of the distance of the electron from the nucleus (r)? Clue: expected value is computed by (r) = forP(r) dr then do integration by parts do sin 0 de | Yn.l.m² (r, $,0)|²r² drarrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², Lz = m₁h, 1 = 0,1,2,..., n 1 - m₁ = 0, ±1, ±2, ..., ±l 3 S² = s(s+1) h² = =h²₁ 4 Consider an excited electron (n > 1) on an H-atom. The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar dependence to some quantum numbers j and m; as J² = j(j + 1)ħ², Jz = mjħ 1 S₂ = m₂h = ± = h Where j and m; are quantum numbers which assume values that jumps in steps of one such that j is non-negative and −j ≤ m¡ ≤ j. For a given quantum number 1, what are the (two) possible values for j? Clue: we can use the vector sum relation of angular momenta, then consider the z-component only.arrow_forwardThe electron in a hydrogen atom is in an exited state for which n = 3. What is the highest frequency that can be radiated? (Given: E1 =-13.6 eV, E2 = -3.40 eV , E3 = -1.51 eV)arrow_forward
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