Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Chapter 42, Problem 10CQ
To determine
The possibility of eight more electrons which allowed in
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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,
L₂ = m₂h,
1 = 0,1,2,..., n-1
m₁ = 0, +1, +2, ..., ±l
3
1
S² = s(s+1)h²=h², S₂ = m₂h = + = h
+/-ħ
4
Consider an excited electron (n > 1) on an H-atom.
What is the minimum angle 0min that the S can have with the z-axis?
Clue: the angle a vector with magnitude V from the z-axis can be computed from
cos 0 = V²/V
How many electrons can occupy the system with l=0, l=2 and l=4. What is number of possible orientations of the orbital angular momentum with l=4? What is the smallest z-component of the orbital angular momentum?
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,
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.
Chapter 42 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 42.3 - Prob. 42.1QQCh. 42.3 - Prob. 42.2QQCh. 42.4 - Prob. 42.3QQCh. 42.4 - Prob. 42.4QQCh. 42.8 - Prob. 42.5QQCh. 42 - Prob. 1OQCh. 42 - Prob. 2OQCh. 42 - Prob. 3OQCh. 42 - Prob. 4OQCh. 42 - Prob. 5OQ
Ch. 42 - Prob. 6OQCh. 42 - Prob. 7OQCh. 42 - Prob. 8OQCh. 42 - Prob. 9OQCh. 42 - Prob. 10OQCh. 42 - Prob. 11OQCh. 42 - Prob. 12OQCh. 42 - Prob. 13OQCh. 42 - Prob. 14OQCh. 42 - Prob. 15OQCh. 42 - Prob. 1CQCh. 42 - Prob. 2CQCh. 42 - Prob. 3CQCh. 42 - Prob. 4CQCh. 42 - Prob. 5CQCh. 42 - Prob. 6CQCh. 42 - Prob. 7CQCh. 42 - Prob. 8CQCh. 42 - Prob. 9CQCh. 42 - Prob. 10CQCh. 42 - Prob. 11CQCh. 42 - Prob. 12CQCh. 42 - Prob. 1PCh. 42 - Prob. 2PCh. 42 - Prob. 3PCh. 42 - Prob. 4PCh. 42 - Prob. 5PCh. 42 - Prob. 6PCh. 42 - Prob. 7PCh. 42 - Prob. 8PCh. 42 - Prob. 9PCh. 42 - Prob. 10PCh. 42 - Prob. 11PCh. 42 - Prob. 12PCh. 42 - Prob. 13PCh. 42 - Prob. 14PCh. 42 - Prob. 15PCh. 42 - Prob. 16PCh. 42 - Prob. 17PCh. 42 - Prob. 18PCh. 42 - Prob. 19PCh. 42 - Prob. 20PCh. 42 - Prob. 21PCh. 42 - Prob. 23PCh. 42 - Prob. 24PCh. 42 - Prob. 25PCh. 42 - Prob. 26PCh. 42 - Prob. 27PCh. 42 - Prob. 28PCh. 42 - Prob. 29PCh. 42 - Prob. 30PCh. 42 - Prob. 31PCh. 42 - Prob. 32PCh. 42 - Prob. 33PCh. 42 - Prob. 34PCh. 42 - Prob. 35PCh. 42 - Prob. 36PCh. 42 - Prob. 37PCh. 42 - Prob. 38PCh. 42 - Prob. 39PCh. 42 - Prob. 40PCh. 42 - Prob. 41PCh. 42 - Prob. 43PCh. 42 - Prob. 44PCh. 42 - Prob. 45PCh. 42 - Prob. 46PCh. 42 - Prob. 47PCh. 42 - Prob. 48PCh. 42 - Prob. 49PCh. 42 - Prob. 50PCh. 42 - Prob. 51PCh. 42 - Prob. 52PCh. 42 - Prob. 53PCh. 42 - Prob. 54PCh. 42 - Prob. 55PCh. 42 - Prob. 56PCh. 42 - Prob. 57PCh. 42 - Prob. 58PCh. 42 - Prob. 59PCh. 42 - Prob. 60PCh. 42 - Prob. 61PCh. 42 - Prob. 62PCh. 42 - Prob. 63PCh. 42 - Prob. 64PCh. 42 - Prob. 65APCh. 42 - Prob. 66APCh. 42 - Prob. 67APCh. 42 - Prob. 68APCh. 42 - Prob. 69APCh. 42 - Prob. 70APCh. 42 - Prob. 71APCh. 42 - Prob. 72APCh. 42 - Prob. 73APCh. 42 - Prob. 74APCh. 42 - Prob. 75APCh. 42 - Prob. 76APCh. 42 - Prob. 77APCh. 42 - Prob. 78APCh. 42 - Prob. 79APCh. 42 - Prob. 80APCh. 42 - Prob. 81APCh. 42 - Prob. 82APCh. 42 - Prob. 83APCh. 42 - Prob. 84APCh. 42 - Prob. 85APCh. 42 - Prob. 86APCh. 42 - Prob. 87APCh. 42 - Prob. 88APCh. 42 - Prob. 89CPCh. 42 - Prob. 90CPCh. 42 - Prob. 91CP
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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/Varrow_forwardYou are working on determining the angle that separates two hybridized orbitals. In the process of determining the coefficients in front of the various atomic orbitals, you align the first one along the z-axis and the second in the x/z-plane (so o = 0). The second hybridized orbital was determined to be: W2 = R1s + R2p, sin 0 + R2p, cos 0 Determine the angle, 0, in degrees to one decimal place (XX.X) that separates these two orbitals. Assume that the angle will be between 0 and 90 degrees.arrow_forwardA hydrogen atom is in the stationary state (n, I, m) = (5, 3, 1) What is the angle between the angular momentum vector L and Lz? Give you answer to 3 significant figures and in units of degrees, but do not include the units in your answer.arrow_forward
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