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.
reciprocal lattices rotates along with the real space lattices of the crystal. true or false?
Deducing the reactants of a Diels-Alder reaction
vn the molecule on the right-hand side of this organic reaction be made in good yield from no more than two reactants, in one
step, by moderately heating the reactants?
?
Δ
O
If your answer is yes, then draw the reactant or reactants in the drawing area below. You can draw the reactants in any
arrangement you like.
• If your answer is no, check the box under the drawing area instead.
Click and drag to start drawing a structure.
Product can't be made in one step.
Explanation
Check
Chapter 11 Solutions
General Chemistry: Principles and Modern Applications (11th Edition)
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