As discussed in Are You Wondering 11-1, the sp hybrid orbitals are algebraic combinations of the s and p orbitals. The required combinations of 2s and 2p orbitals are ψ 1 ( s p ) = 1 2 [ ψ ( 2 s ) + ψ ( 2 p z ) ] ψ 2 ( s p ) = 1 2 [ ψ ( 2 s ) − ψ ( 2 p z ) ] By combining the appropriate functions given in Table 8.2, construct a polar plot in the manner of Figure 8-24 for each of the above functions in the xz plane. In a polar plot the value of ria, set at a fixed value (for example, 1). Describe the shapes and phases of the different portions of the hybrid orbitals, and compare them with those shown in Figure 11-12. Convince yourself that the combinations employing the 2p , or 2p, orbital also give similar hybrid orbitals but pointing in different directions. The combinations for the sp 2 hybrids in the xy plane are ψ 1 ( s p 2 ) = 1 3 ψ ( 2 s ) + 2 3 ψ ( 2 p x ) ψ 2 ( s p 2 ) = 1 3 ψ ( 2 s ) − 1 6 ψ ( 2 p x ) + 1 2 ψ ( 2 p y ) ψ 3 ( s p 2 ) = 1 3 ψ ( 2 s ) − 1 6 ψ ( 2 p x ) − 1 2 ψ ( 2 p y ) By constructing polar plots (in the xy plane), show that these functions correspond to the sp 2 hybrids depicted in Figure 11-10.
As discussed in Are You Wondering 11-1, the sp hybrid orbitals are algebraic combinations of the s and p orbitals. The required combinations of 2s and 2p orbitals are ψ 1 ( s p ) = 1 2 [ ψ ( 2 s ) + ψ ( 2 p z ) ] ψ 2 ( s p ) = 1 2 [ ψ ( 2 s ) − ψ ( 2 p z ) ] By combining the appropriate functions given in Table 8.2, construct a polar plot in the manner of Figure 8-24 for each of the above functions in the xz plane. In a polar plot the value of ria, set at a fixed value (for example, 1). Describe the shapes and phases of the different portions of the hybrid orbitals, and compare them with those shown in Figure 11-12. Convince yourself that the combinations employing the 2p , or 2p, orbital also give similar hybrid orbitals but pointing in different directions. The combinations for the sp 2 hybrids in the xy plane are ψ 1 ( s p 2 ) = 1 3 ψ ( 2 s ) + 2 3 ψ ( 2 p x ) ψ 2 ( s p 2 ) = 1 3 ψ ( 2 s ) − 1 6 ψ ( 2 p x ) + 1 2 ψ ( 2 p y ) ψ 3 ( s p 2 ) = 1 3 ψ ( 2 s ) − 1 6 ψ ( 2 p x ) − 1 2 ψ ( 2 p y ) By constructing polar plots (in the xy plane), show that these functions correspond to the sp 2 hybrids depicted in Figure 11-10.
Solution Summary: The author explains that the hybrid orbital is a combination of the wave function that describes two or more atomic orbitals.
As discussed in Are You Wondering 11-1, the sp hybrid orbitals are algebraic combinations of the s and p orbitals. The required combinations of 2s and 2p orbitals are
ψ
1
(
s
p
)
=
1
2
[
ψ
(
2
s
)
+
ψ
(
2
p
z
)
]
ψ
2
(
s
p
)
=
1
2
[
ψ
(
2
s
)
−
ψ
(
2
p
z
)
]
By combining the appropriate functions given in Table 8.2, construct a polar plot in the manner of Figure 8-24 for each of the above functions in the xz plane. In a polar plot the value of ria, set at a fixed value (for example, 1). Describe the shapes and phases of the different portions of the hybrid orbitals, and compare them with those shown in Figure 11-12.
Convince yourself that the combinations employing the 2p, or 2p, orbital also give similar hybrid orbitals but pointing in different directions.
The combinations for the sp2hybrids in the xy plane are
ψ
1
(
s
p
2
)
=
1
3
ψ
(
2
s
)
+
2
3
ψ
(
2
p
x
)
ψ
2
(
s
p
2
)
=
1
3
ψ
(
2
s
)
−
1
6
ψ
(
2
p
x
)
+
1
2
ψ
(
2
p
y
)
ψ
3
(
s
p
2
)
=
1
3
ψ
(
2
s
)
−
1
6
ψ
(
2
p
x
)
−
1
2
ψ
(
2
p
y
)
By constructing polar plots (in the xy plane), show that these functions correspond to the sp2hybrids depicted in Figure 11-10.
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