4. Calculate for the normalized wavefunction from # 3.
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Transcribed Image Text:25
<r>=
<r> =
4. Calculate <r> for the normalized wavefunction from # 3.
=
24a3-1601
VF Y dz
24a
3. ∙LLOTT
24a-10TT
=(-2)
ao
∞
0
ao
a₂²
e
T
2TT
e
(257) r ( 24²-1 (2- 25 ) (25) ²³ dr [Sinod& faé
鬥
sinodod b
24a-16TT
O
e
€ ²2/20) n²
r³dr HTT
de = r²drsinododo
5. When B-cartene is oxidized in vivo it breaks in half and forms two molecules of retinal (vitamin A), which is a
precursor to the pigment in the retina responsible for vision. The conjugated system of retinal consists of 11 C
atoms and one O atom. In the ground state of retinal, each level up to n-6 is occupied by two electrons.
Assuming that this conjugated system behaves like a particle in a l with an average internuclear distance of 140
pm between each pair of atoms, calculate (a) the separation in energy between the ground state and the first
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