TOPIC: QUANTUM, ATOMIC AND MOLECULAR PHYSICIS In C-C bonds of organic molecules, there are orbitals of carbon atoms with different that degenerate and combine with each other, forming so-called hybridized orbitals that give rise to o-type bonds. Consider hydrogen functions with n = 2, that is, 2s and 2p orbitals of carbon. In sp² hybridization of carbon (as in graphite), these linear combinations i (i = 1, 2, 3) are the following: 4₁ = 4/₂ = 43 = 1 √√34/25 1 √34 1 :42s + -Y2px V 1 √34/25 +. :42px + 1 √2px 1 √6² 1 √642py :42py Note that the 2pz orbital does not participate in this hybridization. Show that the points of maximum probability density for this hybridization are contained in the XY plane and form the vertices of an equilateral triangle whose geometric center is at the origin.

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TOPIC: QUANTUM, ATOMIC AND MOLECULAR PHYSICIS
In C-C bonds of organic molecules, there are orbitals of carbon atoms with different { that degenerate and combine with each
other, forming so-called hybridized orbitals that give rise to o -type bonds. Consider hydrogen functions with n = 2, that is, 2s and
2p orbitals of carbon. In sp hybridization of carbon (as in graphite), these linear combinations ypi (i = 1, 2, 3) are the following:
1
1
1
1
2 =.
22s+
P2px +
Pzpy
1
V3 ==42s +
V3
1
1
Vzpy
V6
Note that the Y2pz orbital does not participate in this hybridization. Show that the points of maximum probability density for this
hybridization are contained in the XY plane and form the vertices of an equilateral triangle whose geometric center is at the
origin.
Transcribed Image Text:TOPIC: QUANTUM, ATOMIC AND MOLECULAR PHYSICIS In C-C bonds of organic molecules, there are orbitals of carbon atoms with different { that degenerate and combine with each other, forming so-called hybridized orbitals that give rise to o -type bonds. Consider hydrogen functions with n = 2, that is, 2s and 2p orbitals of carbon. In sp hybridization of carbon (as in graphite), these linear combinations ypi (i = 1, 2, 3) are the following: 1 1 1 1 2 =. 22s+ P2px + Pzpy 1 V3 ==42s + V3 1 1 Vzpy V6 Note that the Y2pz orbital does not participate in this hybridization. Show that the points of maximum probability density for this hybridization are contained in the XY plane and form the vertices of an equilateral triangle whose geometric center is at the origin.
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