Unit 1, Lesson 03: Answers to Homework
Summary: The “allowed” values for quantum numbers for each principal quantum level “n”:
number of
corresponding
orbitals in this
n
l
ml
ms
sub-level
sub-level
n=1
0
0
+½, -½
1s
1
0
0
2s
1
n=2
+½, -½
1
–1, 0, +1
2p
3
0
0
3s
1
n=3
1
–1, 0, +1
+½, -½
3p
3
2
–2, –1, 0, +1, +2
3d
5
0
0
4s
1
1
–1, 0, +1
4p
3
n=4
+½, -½
2
–2, –1, 0, +1, +2
4d
5
3
–3, –2, –1, 0, +1, +2, +3
4f
7
eg.
33As:
1s
1s22s22p63s23p64s23d104p3
2s
2px 2py 2pz
n= 2
l= 1
ml = 0
ms = - ½
29Cu
1s
3s
n= 2
l= 0
ml = 0
ms = - ½
[Ar] 4s23d104p3
3px 3py 3pz
n= 3
l= 0
ml = 0
ms = +½
1s22s22p63s23p64s13d10
2s
or
2px 2py 2pz
or
3s
n= 3
l= 1
ml = +1
ms = +½
4s
n= 3
l= 1
ml = +1
ms = +½
3dyz 3dxz 3dxy 3dz2 3dx2-y2 4px 4py 4pz
n= 3
l= 2
ml = -2
ms = -½
5s
n= 4
l= 1
ml = 0
ms = +½
[Ar] 4s13d10
3px 3py 3pz
4s
n= 4
l= 0
ml = 0
ms = +½
3dyz 3dxz 3dxy 3dz2 3dx2-y2 4px 4py 4pz
n= 3
l= 2
ml = -1
ms = - ½
5s
Unit 1, Lesson 03: Homework on Quantum Numbers
1. Write the quantum numbers that represent the following electrons:
a) a 5p3 electron would be given the quantum numbers: n = 5 ,
2
l = 1 , ml = +1 and ms = + ½
b) a 3s electron would be given the quantum numbers: n = 3 ,
l = 0 , ml = 0 and ms = - ½
c) a 4f6 electron would be given the quantum numbers: n = 4 ,
l = 3 , ml = +2 and ms = + ½
2. What are the allowable (possible) values for l when:
a) n = 4: l can be 0, 1, 2 or 3 (s, p, d or f)
b) n = 3: l can be 0, 1, or 2 (s, p or d)
c) n = 1: l can be 0 (s)
d) n = 5: l can be 0, 1, 2, 3 or 4 (s, p, d, f or g)
3. What are the allowable (possible) values for ml when:
a) n = 4, l = 3: ml can be -3, -2, -1, 0, +1, +2, +3
b) n = 3, l = 1: ml can be -1, 0, +1
c) n = 2, l = 0: ml can be 0
d) n = 5, l = 4: ml can be -4, -3, -2, -1, 0, +1, +2, +3, +4
4. Write the principal quantum number and letter indicating orbital shape for each of the following:
a) n = 2, l = 1 means 2p
c) n = 4, l = 3 means 4f
e) n = 4, l = 1 means 4p
b) n = 3, l = 2 means 3d
d) n = 1, l = 0 means 1s
f) n = 2, l = 0 means 2s
5. State whether the following sets of quantum numbers are possible (
) or impossible (X):
a) n = 3, l = 3, ml= -1 and ms = + ½
no, when n = 3 then l has a maximum value of 2 (s, p or d)
b) n = 5, l = 2, ml= -1 and ms = - ½
yes, this is the same as the 5d7 electron
c) n = 2, l = 0, ml= 0 and ms = - ½
yes, this is the same as the 2s2 electron
d) n = 3, l = 1, ml= 0 and ms = 0
no, ms must be either + ½ or – ½
e) n = 1, l = 0, ml= +1 and ms = + ½
no, when l = 0 (s) then the orientation ml must also be 0
f) n = 0, l = 0, ml= 0 and ms = + ½
no, n can not be 0
g) n = 4, l = 1, ml= +1 and ms = + ½
yes, this is the same as the 4p3 electron
h) n = 2, l = 1, ml= -2 and ms = - ½
no, when l = 1 (p) then the orientation ml can be –1, 0 or +1
Unit 1, Lesson 03: Answers to Homework
1. Read pages 133 – 138.
2. On page 136, answer questions 1 – 5.
Question 1:
a) n = 5
What are the allowed values for l in each of the following cases?
the allowed values for l are (0…n-1), so l can be 0, 1, 2, 3, 4
(double check: when n = 5, there are 5 types of orbitals: s, p, d, f, g)
b) n = 1
the allowed values for l are (0…n-1), so l can be 0
(double check: when n = 1, there is 1 type of orbital: s)
Question 2: What are the allowed values for ml for an electron with the following quantum numbers?
a) l = 4
the allowed values for ml are (-l…0…+l), so ml can be –4, -3, -2, -1, 0, +1, +2, +3, +4
(double check: l = 4 means the same as the g sublevel, which can have 9 orbitals)
b) l = 0
the allowed values for ml are (-l…0…+l), so ml can only be 0
(double check: l = 0 means the same as the s sublevel, which can have 1 orbital)
Question 3:
What are the names, ml values and total number of orbitals described by the following
quantum numbers?
a) n = 2, l = 0 this represents the second principal quantum level (n=2), and the “s” orbital: 2s
-there is only one ml value: 0 because this represents only one orbital
b) n = 4, l = 3 this represents the fourth principal quantum level (n = 4), and the ‘f’ orbitals: 4f
-there are 7 ml values: -3, -2, -1, 0, +1, +2, +3 so this represents 7 orbitals
Question 4:
Determine the n, l and possible ml values for an electron in the 2p orbital
-the 2 p orbital is in n = 2
-“p” orbitals are indicated by l = 1
-when l = 1, the allowed values for ml are –1, 0, +1
Question 5: Which of the following are allowable sets of quantum numbers for an orbital? Explain.
a) n = 4, l = 4, ml = 0
this is not allowable because l can only have values up to (n - 1)
b) n = 3, l = 2, ml = 1
this is allowable, l is less than n and ml can be any of –2, -1, 0, +1, +2
c) n = 2, l = 0, ml = 0
this is allowable, l is less than n and ml can only be 0
d) n = 5, l = 3, ml = -4
this is not allowable; ml can only have values –3, –2, -1, 0, +1, +2, +3
3. On page 138, answer questions 2, 3, 5, 6.
Question 2:
Quantum Number and Description
1. The Principal Quantum Number (n):
• the allowed values for n are 1, 2, 3 …infinity
2. The Orbital Shape or Angular Momentum
Quantum Number (l):
• the allowed values for l are 0, 1, 2, 3 … (n – 1)
3. The Magnetic Quantum Number (ml):
• the allowed values for ml are – l …. + l
symbol
n
•
l
•
ml
•
What it Describes
describes the size of the quantum
level or how far the electrons are
from the nucleus (their energy)
the shape of the energy sub-levels
(types of orbitals) within each
principal quantum level
indicates the three dimensional
orientation of an electron
Question 3:
n
n=4
l
0
1
2
3
ml
0
–1, 0, +1
–2, –1, 0, +1, +2
–3, –2, –1, 0, +1, +2, +3
4s
4p
4d
4f
1
3
5
7
Question 5: Identify any values that are incorrect:
a) n = 1, l = 1, ml = 0, name 1p
When n = 1, the only allowable value for l is 0, which means ml is also 0 and indicates a 1s orbital
b) n = 4, l = 3, ml = +1, name 4d
The quantum numbers are correct, but the name is not. When l = 3, it indicates an “f” orbital, not d.
c) c) n = 3, l = 1, ml = -2, name 3p
The first two quantum numbers are correct and agree with the name. The value for ml is impossible:
the allowed values when l = 1 are –1, 0, +1.
Question 6:
a) n = 4, l = 1, ml = 0, name 4p
b) n = 2, l = 1, ml = 0, name 2p
c) n = 3, l = 2, ml = -2, name 3d
d) n = 2, l = 0, ml = 0, name 2s
4. Read pages 147 – 150.
5. To see how electron configurations are related to an element’s position on the periodic table, write the
name of the last valence electron of each element (eg. 3d5) in the appropriate square of the Periodic
Table below. Use the predicted electron configurations for Cr, Mo, W, Cu, Ag and Au.
See next page
6.
a)
b)
c)
d)
On the Periodic Table below, label the:
Group numbers and Periods
s,p,d and f blocks of elements
the transition elements and inner-transition elements
Noble gases, Alkali metals, Alkaline Earth metals, and Halogens
Alkali metals
Period ↓
Group→ 1
:
1 1s1
1s2
2 2s1
2s2
3 3s1
3s2
4 4s1
2
3
13
14
15
16
17
18
2p1
2p2
2p3
2p4
2p5
2p6
3p1
3p2
3p3
3p4
3p5
3p6
4s2 3d1 3d2 3d3 3d4 3d5 3d6 3d7 3d8 3d9 3d10
4p1
4p2
4p3
4p4
4p5
4p6
5 5s1
6 6s1
5s2 4d1 4d2 4d3 4d4 4d5 4d6 4d7 4d8 4d9 4d10
5p1
5p2
5p3
5p4
5p5
5p6
6s2 5d1 5d2 5d3 5d4 5d5 5d6 5d7 5d8 5d9 5d10
6p1
6p2
6p3
6p4
6p5
6p6
7s1
7s2 6d1 6d2 6d3 6d4 6d5 6d6 6d7 6d8 6d9 6d10
7p1
7p2
7p3
7p4
7p5
7p6
Inner Transition
Elements
(f block)
4
5
Noble
↓ gases
Halogens
↓
Alkaline Earth metals
6
7
8
9
10
11
12
Transition Elements (d block)
4f1
4f2
4f3
4f4
4f5
4f6
4f7
4f8
4f9
4f10
4f11
4f12
4f13
4f14
5f1
5f2
5f3
5f4
5f5
5f6
5f7
5f8
5f9
5f10
5f11
5f12
5f13
5f14
7. On the page “Nuclear Charge and the Shielding Effect: Explaining the Trends on the Periodic Table”
(handed out in class), for each element complete the:
a) electron configuration
b) Rutherford-Bohr diagram
c) Nuclear charge (the number of protons in the nucleus = atomic number = Z)
d) Shielding effect (the number of electrons in the full shells
between the nucleus and the valence shell)
e) Net Nuclear attraction (the nuclear charge subtract the shielding
effect). Net nuclear attraction is the effective (Zeff) or actual
attraction that exists between a valence electron and the nucleus.
f) Use the numbers on the back of your Periodic Table to complete
the ionization energy (First Ionization Potential, V),
electronegativity and Atomic Radius (∆, Angstroms)
Bring the completed sheet to class for our next lesson!
Shielding Effect