KEY
Practice Problems: Quantum Theory
CHEM 1A
1. Hydrogen has a red emission line at 656.3 nm, what is the energy and frequency of a photon of this
light? Note: Planck’s constant = 6.626 x 10–34 J·s, speed of light = 2.998 x 108 m/s
c
hc
 =
Ephoton = h =


(6.626 x 10–34 J·s) (2.998 x 108 m/s)
Ephoton =
656.3 nm
 =
10–9 m
1 nm
Ephoton = 3.02677861 x 10–19 J
(2.998 x 108 m/s)
10–9 m
656.3 nm
1 nm
 = 4.568032912 x 1014 s–1
3.027 x 10–19 J
Answer (E): ___________________
Answer (): ___________________
4.568 x 1014 s–1 or Hz
2. What is the de Broglie wavelength for an electron moving at 2.42 x 106 m/s?
Note: me = 9.109 x 10–31 kg
 =
 =
h
mu
6.626 x 10–34 J·s
(9.109 x 10–31 kg) (2.42 x 106 m/s)
3.01 x 10–10 m
Answer: ___________________
= 3.00583657 x 10–10 m
many orders of magnitude larger than the diameter of an electron
3. Using the Bohr equation, calculate is the change in energy when an electron transitions from n = 3 to
n= 2 in a hydrogen atom.
E = –2.18 x 10–18 J
E = –2.18 x 10–18 J
Z2
–
n
12
22
Z2
n
–
12
32
E = – 3.02777778 x 10–19 J
– 3.03 x 10–19 J
Answer: ___________________
4. Using the Rydberg formula, calculate the initial energy level when an electron in a hydrogen atom
transitions into n= 2 and emits a photon at 410.1 nm.
Note: the Rydberg constant = 1.097 x 107 m–1
Z2
1
= R

n
1
410.1 nm
–
Z2
n
12
–1
7
= 1.097 x 10 m
10–9 m
1 nm
22
–
12
n
ninit = 6.006428031
n=6
Answer: ___________________
uncertain digit
5. What is the maximum number of electrons that are allowed to have the following set of quantum
numbers in one atom?
n = 4 and ml = +2
4 e–
Answer: ______
only l = 2 (d) and l = 3 (f) on n = 4 can have
ml = +2 orbitals, each of which can hold 2 e–
n = 3 and l = 1
6 e–
Answer: ______
l = 1 (p) has 3 orbitals (ml = –1, 0, +1),
each of which can hold 2 e–
n = 1 and ms = +1/2
1 e–
Answer: ______
n = 1 has 1 sublevel (l = 0 (s)) with 1 orbital
(ml = 0), which can hold 1 spin up e–
6. Provide the possible values for the other three quantum numbers for electrons in n = 3.
Possible Values
l
0
1
2
ml
0
–1, 0, +1
–2, –1, 0, +1, +2
ms
+1/2, –1/2
+1/2, –1/2
+1/2, –1/2
18 e–
Max. # e–: ______
7. What are the four quantum numbers for the last electron in each of the following elements?
Note: Orbital notation (Chapter 8) makes this easier. Assume that ml values fill from more negative to
more positive, and that a spin up e– (ms = +1/2) each fill an orbital before spin down e– begin to pair.
nitrogen
n
l
ml
ms
2
1
+1
+1/2
1
sulfur
3
1
–1
– /2
copper
3
2
+2
–1/2
⥮ ↿↿↿
2s
2p
↿ ⥮⥮⥮⥮↿⇂
4s
3d
⥮ ↿⇂↿ ↿
3s
3p