Quiz 3 Solutions
Quiz 3.1
1. What is the effective nuclear charge felt by a valence electron in a
Fluorine atom? (Note: you do not have to solve the Schrodinger wave
equation unless you want to)
Answer: 9 -2(1) – 6(0.5) = 4
2. Fill in the electrons in the energy level sketch for atomic oxygen below:
3. Sketch a simple 3 dimensional coordinate system and plot out the shape
of a px orbital. Take care to mark the positive and negative lobes. Also,
draw a simple plot of the wavefunction that describes this orbital (in one
dimension), and the corresponding probability distribution plot (in one
dimension).
4.
E=
E=
hc
λ
(6.626 × 10 −34 J ⋅ s) * (3 × 10 8 m s )
−9
268 × 10 m
h2
nh
=
(n f 2 − ni 2 )
ΔE =
2
2
2me r
2me r
2
= 7.42 × 10 −19 J
2
2m
1
ΔE
⋅ 2e = 2
2
r
(n f − ni ) h
2
⎡ (n f 2 − ni 2 ) h2 ⎤
⋅
⎢
⎥
ΔE
2me ⎦
⎣
1
2
=r
⎡ (5 2 − 0 2 )
(6.626 × 10 −34 J ⋅ s)2 ⎤
r=⎢
⋅
⎥
−19
2
−31
⎣ 7.42 × 10 J 8π ⋅ 9.109 × 10 kg ⎦
d = 2r = 9.08 × 10 −10 m = 9.08Α
1
2
= 4.54 × 10 −10 m
CHEM 202
20min
Quiz 3.2
09/14/07
1.
a)Fill the following electron diagram of carbon and oxygen with the correct amount of
electrons and correct spin according to Hund’s Rule. Indicate how many unpaired
electrons there are for each atom.
Carbon:
1s
2s
2p
Amount of unpaired e- = 2
Oxygen:
1s
2s
2p
Amount of unpaired e- = 2
b) How would the amount of unpaired e- change for carbon and oxygen if the 2s orbital
and 2p orbital are the same energy (if they are degenerate)?
Carbon increase to 4, oxygen stay at 2
2. Draw the pz orbital in the provided axis. Be sure to correctly shade the orbital to
indicate sign. Indicate where the node(s) is located and write down how many total
nodes there are in this orbital.
z
1 node
x
y
1 node total
3. The treatment of a particle in a one-dimensional box can be extended to a twodimensional box of dimensions Lx and Ly yielding the following expression for energy:
2
2
ny ⎞
h 2 ⎛⎜ n x
⎟
Ex,y =
+
8m ⎜⎝ L x 2 L y 2 ⎟⎠
The two quantum numbers nx, and ny are independent and can only assume integer
values.
a) Determine the quantum number combinations (nx, ny) of the four lowest levels
assuming that the box is square (Lx=Ly). (Hint: Some combinations can have the same
energy)
Ground: (1,1) 1st excited: (1,2) (2,1) 2nd excited: (2,2) 3rd excited: (3,1) (1,3)
b) In a box with Lx=Ly=10 nm, what is the energy change if an electron makes a
transitions from the 2nd excited state to the 3rd excited state. (2,2) Æ (3,1)
(
)
2
h2
h2
h2
6.626 × 10 −34
ΔE =
[(9 + 1) − (4 + 4)] = 2 (2) =
=
= 1.2 × 10 − 21 J
2
2
−31
−9
8mL
8mL
4mL
4 × 9.101 × 10 × 10 × 10
(
)
Quiz 3.3
CHEM 202
20min
1)
Zeff=Zact-Ncore-0.5(Nvalence-1)
a. 1s22s22p63s23p6 Zeff=17-10-0.5*(8-1) =3.5
b. 1s22s22p2 Zeff=6-2-0.5*(4-1)=2.5
c. 1s22s22p6 Zeff=12-10-0.5*(0-1)= 2.5
2)
3)
See Next Page
Atomic Nitrogen
4) See Next Page
09/14/07