6-42
6-43
6-44
See answer to problem 6-42 to see calculation method.
a) 656.467nm
b) 102.573 nm
c) 4052.27 nm
d) not an emission
e) not an emission
f) not an emission
The transition from n=5 to n=4 results in the emission of light with the longest wavelength.
6-45
a. 6560467 nm
b. 486.282 nm
c. 97.2544 nm
d. not an absorption
e. not an abasorption
f. not an absorption
The shortest wavelength is the highest energy.
The transition from n=1 to n=4 would result in the absorption of a proton with the largest energy.
6-46
When identified with respect to the Bohr model, the Lyman series of lines are in the
ultraviolet because or the transition to the n = 1 electron configuration. The Balmer series
represents transitions to n = 2, which are energetically associated with the visible region of
the spectrum. Paschen, Bracket, and Pfund line series can be associated with transitions to
n = 3, 4, 5 from the successively higher levels. The energies become less as the terminating
n increases. These higher n terminating series involve transitions which must be less
energetic than those of the visible region of the spectrum. Their occurrence in the infrared
region is therefore in harmony.
6-47
6-48
Four quantum numbers parametrize our model describing the electron configurations of
atoms.
n principal quantum number -- characterizes the energy of the electron configuration and
it characterizes the size of the region of space where the model predicts the electron should
most probably be found.
l angular momentum quantum number -- characterizes the shape of the region of space
where the model predicts the electron should most probably be found.
m magnetic quantum number -- characterizes the direction relative to a magnetic field of
the region of space where the model predicts the electron should most probably be found.
s spin quantum number -- is associated with the specific properties of the individual
electron which occupies the region of space where the model predicts the electron should
most probably be found.
6-49
The selection rules for the four quantum numbers are
n integer values 1,2,3,4,5,6....
l integer values 0,1,2,3,4,5, ..., n-1
m integer values -l,-(l-1)..., 0, ..., (l-l), l
s +1/2, -1/2
6-50
a. n
b. l
c. m
d. s
6-51
When the principal quantum number, n, equals 4, the angular momentum quantum number,
l, is allowed values of 0, 1,2, 3 by our model. According to out model, orbitals with the
same value of n have similar energy and distance relative to the nucleus. The differing l
values relate to differing shapes associated with the mathematical presentation of a
description of the space where the model predicts the specified electron should most likely
be found. You are invited to refer to the text for pictorial presentation of an artistic rendition
of one persons view of the differences.
6-52
When the angular momentum quantum number, l, is 2, our model allows the magnetic
quantum number, m, to have the values of -2, -1,0, 1, 2. In the presence of a magnetic field
(which has the property of presenting a direction of reference) the magnetic quantum
number can be associated with relative orientation of the region of space where the model
suggests that an electron would most probably be found.
6-53
The allowed values of s are +1/2 and -1/2.
6-54
The allowed values of m are -2, -1,0, 1, 2 when l = 2
6-55
The maximum value of the angular quantum number. l, is 3 when n=4
6-56
a) l must be positive
b) m cannot be larger than the value of
c) s must have a value of +1/2 or-1/2
d) legitimate
6-57
a) n must be a positive integer, in this case, n should = 1
b) legitimate
c) l cannot be greater than n-1
d) m cannot be larger in magnitude than + or - l
e) s must have a value of +1/2 or -1/2
6-58
Our model requires that no more than 2(2l+1) electrons can be accommodated in orbitals
with a given angular momentum. for l = 3, the number of corresponding electrons can be 14.
6-59
According to our model of the electron configuration of an atom, the total number of orbitals
having a specified quantum number, n, is n2. If the electron spin is restricted to a single
value of +1/2, there can be 16 electrons with principal quantum number 4.
6-60
n l m s
1 0 0 1/2
1 0 0 -1/2
2 0 0 1/2
2 0 0 -1/2
2 1 0 1/2
2 1 0 -1/2
2 1 1 1/2
2 1 1 -1/2
2 1 -1 1/2
2 1 -1 -1/2
6-61
| n | l | m | s | |
| 1 | 0 | 0 | 1/2 | |
| 1 | 0 | 0 | -1 | |
| 1 | 1 | 0 | 1 | |
| 1 | 1 | 0 | -1 | |
| 1 | 1 | 1 | 1 | |
| 1 | 1 | 1 | -1 | |
| 1 | 0 | 0 | -1 | |
| 1 | 0 | 0 | 1 |
6-62
As the value of the principal quantum number, n, becomes large the difference in the energy
of the subshells becomes very small.
6-63
| l | symbol |
| 0 | s |
| 1 | p |
| 2 | d |
| 3 | f |
6-64
number of orbitals = (3)2=9 for n=3
number of orbitals = (4)2=16 for n=4
number of orbitals = (5)2=25 for n=5
6-65
a) describes a 2p orbital
b) describes a 2s orbital
c) describes a 2d orbital
d) describes a 3d orbital
e) describes a 3p orbital
6-66
c. a 2d orbital cannot exist
6-67
max number of electrons n
2 1
2(2)2 = 8 2
2(3)2 = 18 3
2(4)2 = 32 4
2(5)2 = 50 5
6-68
all d subshells can accommodate 10 electrons
6-69
5 unpaired electrons can be placed in a d subshell.
6-70
The difference between atomic number of any adjacent pair of elements in a group of the
periodic table will be 8, 18, or 32 because the change between members of a group
corresponds to a change in principal quantum number.
6-71
For a given value of n there are (n-l) possible values of l. For each value of l there are
2(l)+1 orbitals predicted by the model. When these terms are summed the result is n2.
6-72
Since each orbital can hold two electrons and there are n2 orbitals predicted by the model.
The maximum number of electrons allowed is 2n2.
6-73
The number of orbitals in a subshell is derived from the allowed values of the magnetic
quantum number, m. There are 2(l)+1 allowed values where l is the angular momentum
quantum number.
6-74
a. n and l
The size and shape of an orbital determine the energy.
6-75
c is correct
6-76
e is incorrect.
6-77
As atomic orbitals are filled according to the aufbau principle, the 6p orbitals are filled
immediately after the 5d orbitals.
6-78
Orbitals are degenerate when the (d) have the same energy.
6-79
filling of s orbitals groups 1 and 2
filling of p orbitals groups 13 - 18
filling of d orbitals groups 3 - 12
filling of f orbitals inner transition elements
6-80
Na [Ne] 3s1
Mg [Ne] 3s2
AI [Ne] 3s2 3p1
Si [Ne] 3s2 3p2
P [Ne] 3s2 3p3
S [Ne] 3s2 3p4
Cl [Ne] 3s2 3p5
Ar [Ne] 3s2 3p6 = [Ar]
6-81
6-82
6-83
x=2
6-84
(b) satisfies Hund's rules for hte electronic configuration of carbon.
6-85
(b) is correct for the electronic configuration of the P3- ion.
6-86
(c) is correct for the electronic configuration of the Br- ion.
6-87
Vanadium has 23 electrons total, n=3 for 11 electrons
6-88
6 electrons in s orbitals in the V2+ ion.
6-89
Zn has the largest number of electrons for n = 3
6-90
n=4, l=1,m=1, and s=1/2 represents the last electron added to form a gallium ion.
6-91
n = 3, l = 2, m = 0, and s = 1/2 represents the last electron added to form an As3+ ion.
6-92
Element 114 should be placed in group 14 below lead.
6-93
n=5 l=4
6-94
Y is the first element to have 4d electrons in its electronic configuration.
6-95
lanthanides correspond to l = 3
6-96
P has the largest number of unpaired electrons.
6-97
Fe3+ has five unpaired electrons.
6-
6-99
ddu = (-1/3)+(-1/3)+(2/3) = 0
duu = (-1/3)+(2/3)+(2/3) = 1
ddu = neutron
duu = proton