College Physics
2nd Edition
ISBN: 9780134601823
Author: ETKINA, Eugenia, Planinšič, G. (gorazd), Van Heuvelen, Alan
Publisher: Pearson,
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Chapter 28, Problem 47P
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For what energy levels in the hydrogen atom will we
not find l
2 states?
=
3.
eV.
Consider an atom of triply ionized beryllium Be³+ with an energy of -9.704
(a) List all the possible states, excluding spin, of the hydrogen atom with this energy.
(b) What is the degree of degeneracy?
(c) What is the maximum possible angular momentum L (as a multiple of ħ)?
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 28 Solutions
College Physics
Ch. 28 - Prob. 1RQCh. 28 - Prob. 2RQCh. 28 - Prob. 3RQCh. 28 - Prob. 4RQCh. 28 - Prob. 5RQCh. 28 - Prob. 6RQCh. 28 - Prob. 7RQCh. 28 - Prob. 8RQCh. 28 - Prob. 1MCQCh. 28 - Prob. 2MCQ
Ch. 28 - Prob. 3MCQCh. 28 - Prob. 4MCQCh. 28 - Prob. 5MCQCh. 28 - Prob. 6MCQCh. 28 - Prob. 7MCQCh. 28 - Prob. 8MCQCh. 28 - Prob. 9MCQCh. 28 - Prob. 10MCQCh. 28 - Prob. 11MCQCh. 28 - Prob. 12MCQCh. 28 - Prob. 13CQCh. 28 - Prob. 14CQCh. 28 - Prob. 15CQCh. 28 - Prob. 16CQCh. 28 - Prob. 17CQCh. 28 - Prob. 18CQCh. 28 - Prob. 19CQCh. 28 - Prob. 20CQCh. 28 - Prob. 21CQCh. 28 - Prob. 22CQCh. 28 - Prob. 23CQCh. 28 - Prob. 24CQCh. 28 - Prob. 25CQCh. 28 - Prob. 26CQCh. 28 - Prob. 27CQCh. 28 - Prob. 28CQCh. 28 - Prob. 29CQCh. 28 - Prob. 30CQCh. 28 - Prob. 31CQCh. 28 - Prob. 32CQCh. 28 - Prob. 33CQCh. 28 - Prob. 34CQCh. 28 - Prob. 1PCh. 28 - Prob. 2PCh. 28 - Prob. 3PCh. 28 - Prob. 4PCh. 28 - Prob. 5PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 12PCh. 28 - Prob. 13PCh. 28 - Prob. 14PCh. 28 - Prob. 15PCh. 28 - Prob. 16PCh. 28 - Prob. 17PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - Prob. 21PCh. 28 - Prob. 22PCh. 28 - 28.4 Lasers (a) A laser pulse emits 2.0 J of...Ch. 28 - Prob. 24PCh. 28 - Prob. 25PCh. 28 - Prob. 26PCh. 28 - Prob. 27PCh. 28 - Prob. 28PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 31PCh. 28 - Prob. 32PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - Prob. 37PCh. 28 - Prob. 38PCh. 28 - Prob. 39PCh. 28 - Prob. 40PCh. 28 - Prob. 41PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - Prob. 45PCh. 28 - Prob. 46PCh. 28 - Prob. 47PCh. 28 - Prob. 48PCh. 28 - Prob. 49PCh. 28 - Prob. 50PCh. 28 - Prob. 51PCh. 28 - Prob. 52PCh. 28 - Prob. 53PCh. 28 - Prob. 54PCh. 28 - Prob. 55PCh. 28 - Prob. 56PCh. 28 - Prob. 57PCh. 28 - Prob. 58PCh. 28 - Prob. 59GPCh. 28 - Prob. 60GPCh. 28 - Prob. 61GPCh. 28 - Prob. 62GPCh. 28 - Prob. 63GPCh. 28 - Prob. 64GPCh. 28 - Prob. 65GPCh. 28 - Prob. 66GPCh. 28 - Prob. 67GPCh. 28 - Prob. 68RPPCh. 28 - Prob. 69RPPCh. 28 - Prob. 70RPPCh. 28 - Prob. 71RPPCh. 28 - Prob. 72RPPCh. 28 - Prob. 73RPPCh. 28 - Prob. 74RPPCh. 28 - Prob. 75RPPCh. 28 - Prob. 76RPPCh. 28 - Prob. 77RPPCh. 28 - Prob. 78RPP
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- What are the possible values of m for an electron in the n = 4 state?arrow_forwardA hydrogen atom is in the 4d state. a) What is the magnitude of the orbital angular momentum? b) Calculate the possible values of the total angular momentum quantum number. c) Calculate the magnitude of the total angular momentum for each value in (b).arrow_forwardHow 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?arrow_forward
- 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?arrow_forwardIn another universe, the electron is a spin@3/2 rather than a spin@1/2 particle, but all other physics are the same as in our universe. In this universe what is the ground-state electron configuration of sodium?arrow_forwardc. n= 2, 1 = 0. 2. Calculate the maximum number of electrons that can occupy a shell with (a) n = 2, (b) n = 3, and (c) n as a variable. Note you are only looking at the orbitals with the specified n value, not those at lower energies.arrow_forward
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- Calculate the energy of an electron in the n = 3 state in a hydrogen atom. a) 2.42 × 10-19 J d) −7.27 × 10-19 J b) −2.42 × 10-19 J e) −6.54 × 10-18 J c) 7.27 × 10-19 Jarrow_forwardWhat are the possible values of m1 for an electron in the n=4 state?arrow_forwardThe allowed energies of a simple atom are 0.0 eV, 4.0 eV, and 6.0 eV. An electron traveling at a speed of 1.5x106 m/s collisionally excites the atom. Part A) What is the minimum speed the electron could have after the collision? Part B) What is the maximum speed the electron could have after the collision?arrow_forward
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