Chem 2 AP Homework #7-4: Problems pg. 299 #57, 58, 61, 62, 63, 67, 71, 77, 80, 83, 91, 124
57
Discuss the similarities and differences between a 1s and a 2s orbital.
A 2s orbital is larger than a 1s orbital. Both have the same spherical shape. The 1s orbital is lower in
energy than the 2s.
58
What is the difference between a 2p x and a 2p y orbital?
The two orbitals are identical in size, shape, and energy. They differ only in their orientation with respect
to each other.
61
Calculate the total number of electrons that can occupy (a) one s orbital; (b) three p orbitals; (c)
five d orbitals; (d) seven f orbitals.
There can be a maximum of two electrons occupying one orbital.
(a) two
(b) six
(c) ten
(d) fourteen
The Pauli exclusion principle demands a maximum of two electrons per orbital. All orbitals of the same
type in the same energy level have the same energy and differ only in their orientation. All sublevels of
the same designation hold the same number of electrons.
62
What is the total number of electrons that can be held in all orbitals having the same principal
quantum number n?
n value
orbital sum
total number of electrons
1
1
2
2
1+3=4
8
3
1+3+5=9
18
4
1 + 3 + 5 + 7 = 16
32
5
1 + 3 + 5 + 7 + 9 = 25
50
6
1 + 3 + 5 + 7 + 9 + 11 = 36
72
In each case the total number of orbitals is just the square of the n value (n2). The total number of
electrons is 2n 2.
63
Determine the maximum number of electrons that can be found in each of the following
subshells: 3s, 3d, 4p, 4f, 5f.
The maximum number of electrons that can be found in the following subshells is:
3s: two
3d: ten
4p: six
4f: fourteen
5f: fourteen
67
For each of the following pairs of hydrogen orbitals, indicate which is higher in energy: (a) 1s,
2s; (b) 2p, 3p; (c) 3d xy, 3d yx; d) 3s, 3d; (e) 4f, 5s.
In hydrogen, the energy does not depend on the orbital type, only on the principal quantum number n.
If two orbitals in the hydrogen atom have the same value of n, they have equal energy.
(a) 2s > 1s
71
(b) 3p > 2p
(c) 3dxy = 3dyz
(d) 3s = 3d
(e) 5s > 4f
What is electron configuration? Describe the roles that the Pauli exclusion principle and
Hund’s rule play in writing the electron configuration of elements.
Electron configuration is the arrangement of electrons in the orbitals of an atom. The Pauli exclusion
principle allows a maximum of two electrons in any single orbital; Hund’s rule states that, when filling
orbitals of equal energy (degenerate), all orbitals are half filled before any orbital is completely filled.
2
HOMEWORK #7-4 ANSWER KEY
77
Explain what is meant by a noble gas core. Write the electron configuration of a xenon core.
A noble gas core is the electron configuration of the noble gas immediately preceding the atom of
interest and represents the inner electrons. For [Xe], the configuration would be
1s22s22p63s23p64s23d104p65s24d105p6.
80
The ground-state electron configurations listed here are incorrect. Explain what mistakes have
been made in each case and write the correct electron configurations.
Al: 1s 22s 22p 43s 23p 3 There are not enough electrons in the 2p subshell. (The 2p subshell holds six
electrons.) The number of electrons (13) is correct. The electron configuration should be
1s22s22p63s23p1. The configuration shown might be an excited state of an aluminum atom.
B: 1s 22s 22p 5 There are too many electrons. (Boron only has five electrons.) The electron configuration
should be 1s22s22p1. What would be the electric charge of a boron ion with the electron arrangement
given in the problem?
F: 1s 22s 22p 6 There are also too many electrons. (Fluorine only has nine electrons.) The configuration
shown is that of the F ion. The correct electron configuration is 1s22s22p5.
−
83
Write the ground-state electron configurations for the following elements: B, V, Ni, As, I, Au
B: 1s22s22p1
As: [Ar]4s23d104p3
V: [Ar]4s23d3
I:
[Kr]5s24d105p5
Ni: [Ar]4s23d8
Au: [Xe]6s24f145d9 (actually 6s14f145d10 due to an exception)
91
Use the Aufbau principle to obtain the ground-state electron configuration of selenium.
Se: [Ar]4s23d104p4
124
Shown below are portions of orbital diagrams representing
the ground-state electron configurations of certain elements.
Which of them violate the Pauli exclusion principle? Hund’s
rule?
The Pauli exclusion principle states that no two electrons in an
atom can have the same four quantum numbers. In other words,
only two electrons may exist in the same atomic orbital, and these
electrons must have opposite spins. (a) and (f) violate the Pauli
exclusion principle.
Hund’s rule states that the most stable arrangement of electrons in subshells is the one with the greatest
number of parallel spins. (b), (d), and (e) violate Hund’s rule. (In b and e, the single spin-down
electron is considered a higher-energy state.)
(c) is a valid configuration (no rule requires the first paired electron to be in the first p-orbital).