1 (299)

Prévia do material em texto

SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 291
Solutions to problems
P9A.2 For the purposes of this problem, the px orbital has the same properties as a unit
vector along the x-axis and the py orbital is likewise a unit vector along the y-
axis.�e hybrid orbital ψ is represented by a vector resulting from the addition
of the vectors representing the px and py orbitals. �e s orbital is spherically
symmetric about the origin, therefore it has no e�ect on the direction of the
hybrid.
x
y
√
3
2py
−
√
1
2px
ψ
βα
�e angle α is calculated as
α = tan−1 (
√
3/2/
√
1/2) = tan−1
√
3 = 60○
�erefore the vector representingψmakes and angle β = 180○−α = 180○−60○ =
120○ to the x-axis.
P9A.4 Following the same logic as in Problem P9A.2 and Problem P9A.2, the vector
representation of the two hybrid atomic orbitals is as shown below.
h1
h2
x
y
θ/2
It follows from the diagram that for h1 the contribution from px is proportional
to cos θ/2, and the contribution from py is proportional to sin θ/2; for h2 all
that is di�erent is that the sign of the contribution from py is reversed. Both
hybrids will have a contribution from the s orbital, and so can be written
h1 = s+λ (cos(θ/2)px + sin(θ/2)py) h2 = s+λ (cos(θ/2)px − sin(θ/2)py)