PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
6th Edition
ISBN: 9781429206099
Author: Tipler
Publisher: MAC HIGHER
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Chapter 36, Problem 10P
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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,
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.
Consider the atom having the electron configuration 1s2 2s2 2p6 3s2. Assume that the z components of both the orbital abd spin angular momenta of the electron in the 3p subshell are positive. What are the quantum numbers that describe the state of this electron.
n=3 l=1 m=-1 s=1/2n=3 l=1 m=2 s=1/2n=3 l=2 m=1 s=1/2n=3 l=1 m=1 s=1/2n=3 l=2 m=2 s=-1/2
Can we say which one is correct?
Zirconium (Z= 40) has two electrons in an incomplete d sub-
shell. (a) What are the values of n and e for each electron?
(b) What are all possible values of me and m? (c) What is the
electron configuration in the ground state of zirconium?
Chapter 36 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
Ch. 36 - Prob. 1PCh. 36 - Prob. 2PCh. 36 - Prob. 3PCh. 36 - Prob. 4PCh. 36 - Prob. 5PCh. 36 - Prob. 6PCh. 36 - Prob. 7PCh. 36 - Prob. 8PCh. 36 - Prob. 9PCh. 36 - Prob. 10P
Ch. 36 - Prob. 11PCh. 36 - Prob. 12PCh. 36 - Prob. 13PCh. 36 - Prob. 14PCh. 36 - Prob. 15PCh. 36 - Prob. 16PCh. 36 - Prob. 17PCh. 36 - Prob. 18PCh. 36 - Prob. 19PCh. 36 - Prob. 20PCh. 36 - Prob. 21PCh. 36 - Prob. 22PCh. 36 - Prob. 23PCh. 36 - Prob. 24PCh. 36 - Prob. 25PCh. 36 - Prob. 26PCh. 36 - Prob. 27PCh. 36 - Prob. 28PCh. 36 - Prob. 29PCh. 36 - Prob. 30PCh. 36 - Prob. 31PCh. 36 - Prob. 32PCh. 36 - Prob. 33PCh. 36 - Prob. 34PCh. 36 - Prob. 35PCh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Prob. 55PCh. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75P
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- What are the possible values of m for an electron in the n = 4 state?arrow_forwardAn electron in an atom is in a state with / = 4. What is the minimum angle between L (angular momentum vector) and the z-axis?arrow_forwardHow many electron states are there in the following shells: (a) n = 4, (b) n = 1, (c) n = 3, (d) n = 2?arrow_forward
- 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_forward(a) What is the magnitude of the angular momentum for an l = 3 electron? (b) Calculate the magnitude of the electron’s spin angular momentum. (c) What is the ratio of these angular momenta?arrow_forwardHow many different possible states can there be for an atom with n =5 and l = 1 ?arrow_forward
- An electron is in the n = 4, l = 3 state of the hydrogen atom. (a) What is the length of the electron's angular momentum vector? (b) How many different possible z components can the angular momentum have? List the possible z components. (c) What are the values of the angle that the angular momentum vector, L, makes with the z-axis? (d) Would your answers to (a), (b) or (c) change if the principal quantum number were n = 5 instead of n = 4?arrow_forwardAn 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?arrow_forwardAn electron in the n = 3 state in hydrogen has orbital angular momentum 1.49 x 10-34 J s 1.49 x 10-34 Js 2.58 x 10-34 J s All 3 are possiblearrow_forward
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