14-20.
B
2
2*5 = 10 electrons
 g
  2  * u
  2  g
  2  * u
  2  u
  2 bond order = ½ (6-4) = 1
C
2
2*6 = 12 electrons
 g
  2  * u
  2  g
  2  * u
  2  u
  4 bond order = ½ (8-4) = 2
Since the bond order is higher for C
2
, it will have a greater dissociation energy.
14-24.
NO 7+8 = 15 electrons
 g
  2  * u
  2  g
  2  * u
  2  u
  4  g
  2  * g
  1 bond order = ½ (10-5) = 2.5
N
2
2*7 = 14 electrons
 g
  2  * u
  2  g
  2  * u
  2  u
  4  g
  2 bond order = ½ (10-4) =3
Since the bond order is higher for N
2
, it will have the shorter bond length.
14-25.
CO 6+8=14 electrons
NO 7+8=15 electrons
CN 6+7+1=14 electrons
 g
 g
  2  * u
  2  g
  2  * u
  2  u
  4  g
  2
  2  * u
  2  g
  2  * u
  2  u
  4  g
  2  * g
  1
 g
  2  * u
  2  g
  2  * u
  2  u
  4  g
  2
Question 19-2.
Doppler broadening. This contribution to the linewidth is due to the Doppler effect which shifts the frequency of the radiation emitted or absorbed when the atoms or molecules involved are moving towards or away from the detecting device. Molecules have a wide range of speeds in all directions in a gas and the detected spectral line is the absorption or emission profile arising from all the resulting Doppler shifts. The shape of a Doppler-broadened spectral line reflects the Maxwell distribution of speeds in the sample at the temperature of the experiment; hence the line broadens as the temperature is increased because the molecules acquire a wider range of speeds. Therefore, to decrease the linewidth, the temperature of the sample should be decreased.
Lifetime broadening. The Doppler broadening is significant in gas-phase samples, but lifetime broadening occurs in all states of matter. This kind of broadening is a quantum mechanical effect related to the uncertainty principle and is due to the lifetimes of the states involved in the transition.
Pressure (or collisional) broadening. Collisions between molecules can deactivate excited states and therefore affect the lifetime of the excited states. Lowering the pressure can reduce pressure broadening.

19-1.
λ = 442 nm a)
 b)
 c


 
 c
3.00*10 8 m s
442*10  9 m
6.79*10 14 s
 1
3.00*10 10
 6.79*10 14 s
 1
 22620 cm
 1
19-21. a) line width 0.1 cm -1
0.1
cm
 1 * hc
 0.1
cm
 1 6.626*10  34
J s 3.00*10 10 /  1.99*10  24
J

4 
4 h
 h

E

6.626*10  34
  24
J
 2.65*10  11 s
 26.5
ps b) line width 1 cm -1
1 cm
 1 * hc
 1 cm
 1 6.626*10  34
J s 3.00*10 10 /  1.99*10  23
J

4 h

4  h

E

6.626*10  34
  23
J c) line width 1.0 GHz
1
GHz
 1*10 9 s
 1
1*10 9 s
 1 * h
 1*10 9 s
 1
 2.65*10  12 s
 2.65
ps
6.626*10  34 *  6.626*10  25
J

4 h

4  h

E

6.626*10  34
  25
J
 7.96*10  11 s
 79.6
ps

19-22. a)
1*10 13
1
 1*10  13 /

4 h

4 h


6.626*10  34 *
 13 s hc
 5.27*10  22
J
5.27*10  22
J
6.626*10  34
J s 3.00*10 10 cm s
 26.5
cm
 1 b)
1*10 13
1
*
200 collisions
1 effective collision
 2*10  11 s /effective collision

4 h

4 h
 

6.626*10  34
   11 s hc
 2.64*10  24
J
2.64*10  24
J
6.626*10  34
J s 3.00*10 10 cm / s
 0.133
cm
 1
#3.
  5.52*10 13 s
 1
6.5*10 7 s
 1

RT ln2 c M

1/2
6.5*10 7 s
 1 
2*5.52*10
3.00*10 8
13
/ s
 1



*

* *ln2
98.916*10  3 


1/2
T
 268 K
#4.
B
2
+ 5+5-1 = 9 electrons
Molecular orbital electron configuration:
 g
Bond order = ½ (5-4) = ½
One unpaired electron → paramagnetic
Term symbol:
 Only partially filled orbital:
 u
 m l
= +1 → M
L
= 1
 m s
= ½ → M
S
= ½
 electron is “u”
 term symbol = 2 Π u
  1
  2  * u
  2  g
  2  * u
  2  u
  1

#5.
NO 7+8 = 15 electrons
Molecular orbital electron configuration:
   2  *
    2  *
      2  *
  1
Bond order = ½ (10-5) = 2½
One unpaired electron → paramagnetic
Term symbol:
 Only partially filled orbital:
 *
  1
 m l
= +1 → M
L
= 1
 m s
= ½ → M
S
= ½
 heteronuclear molecule, so no g/u subscript
 term symbol = 2 Π
#6.
 g
  2  * u
  2  g
  2  * u
    1
Only partially filled subshells are:
 u
*
For
 u
*
  1
, m l
= 0
    1
For
 u
  1
, m l
= ±1
M
L
  m l
For the electrons spins, these possibilities: u
(2p)
* u
(2s)
M
S
=1 M
S
=1 M
S
=0 M
S
=0
M
S
= | m s
|
And, for the two electrons, u * u = odd * odd = even = g
The possible term symbols are then 1 Π g
3 Π g
From Hund’s Rule, the higher multiplicity has lower energy, so 3 Π g
is lowest in energy.