BioPHYSICAL chemistry

12.10 Calculate the wavelength of light absorbed when an electron makes a transition from an
n=3 state to an n=1 state in copper.
12.11 Write in integral form (but do not solve) the expectation value of radius for the 2s state.
12.12 Write in integral form (but do not solve) the expectation value of momentum for the 2s
state.
12.13 Write (but do not solve) the probability of finding an electron in the 2s state beyond a
radius of 3a 0.
12.14 How is the pxorbital related to wavefunctions obtained using Schrödinger’s equation?
12.15Determine the probability of finding an electron in the 1s state beyond a distance of 1.058 Å.
12.16 Determine the probability of finding an electron in the 1s state between a distance of
0.529 Å and 1.058 Å.
12.17 Calculate the most probable radius for the 1s state using the wavefunction.
12.18 Calculate the expectation value of the radius for the 1s state.
12.19 Explain how the wavefunction for an electron in a 2s orbital can have a value of zero.
12.20 Schrödinger’s equation can be divided into three parts using the separation of variables.
The φdependence is given by Φ(φ) =Aeimlφ. Demonstrate why the value of mlmust be an
integer.
12.21 Demonstrate that the function Φ(φ) = Aeimlφ is a solution to the phi dependence of
Schrödinger’s equation:

12.22 Demonstrate that the function Θ(θ) =Bcosθis a solution to the theta dependence of
Schrödinger’s equation when l=1 and ml=0:

12.23 Determine the energy of the wavefunction Π(r) =re−αrwhere by substituting

this function into the radial form of the Schrödinger equation when l=0:

12.24 Explain how the wavefunction is related to the boundary surface of an orbital.
12.25 What transitions are forbidden due to the fact that photons have a spin of 1?
12.26 (a) Write Schrödinger’s equation for the hydrogen atom if the classical potential energy
between a positive and negative charge was given by

(b) What can be predicted about the energies of the wavefunctions for this modified potential?

Vr

e

o r

(, , )

cos

θφ

πε

θ

=

−^2

4 3

d

d

2

22

2

0

12

r 4

r

ll

r

me

r

Π()

()

+−

+

+

⎛

⎝

⎜⎜

⎞

⎠

⎟

Z πε ⎟⎟

ΠΠ()r = ()

m

Er

2

Z

α

πε

=

me

Z^2

2

(^40)
sin sin

()

θ [( )sin

θ

θ

θ

θ

θ

d

d

d

d

⎡ Θ

⎣

⎢

⎢

⎤

⎦

⎥

⎥

++ll 1 2 −−=ml^2 ]()Θθ 0

d

d

2

2

2

φ

ΦΦ()φφ=−ml ()

268 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY