Unit 1, Lesson 03: Answers to Homework

Summary: The “allowed” values for quantum numbers for each principal quantum level “n”:

n l ml ms corresponding

sub-level

number of

orbitals in this

sub-level

n = 1 0 0 + ½ , - ½ 1s 1

n = 2 0

1

0

–1, 0, +1 + ½ , - ½

2s

2p

1

3

n = 3

0

1

2

0

–1, 0, +1

–2, –1, 0, +1, +2

+ ½ , - ½

3s

3p

3d

1

3

5

n = 4

0

1

2

3

0

–1, 0, +1

–2, –1, 0, +1, +2

–3, –2, –1, 0, +1, +2, +3

+ ½ , - ½

4s

4p

4d

4f

1

3

5

7

eg. 33As: 1s22s

22p

63s

23p

64s

23d

104p

3 or [Ar] 4s

23d

104p

3

1s

2s

2px

2py

2pz

3s 3px

3py

3pz

4s 3dyz 3dxz 3dxy 3dz2 3dx2-y2 4px

4py

4pz

5s

29Cu 1s22s

22p

63s

23p

64s

13d

10 or [Ar] 4s

13d

10

1s

2s

2px

2py

2pz

3s 3px

3py

3pz

4s 3dyz 3dxz 3dxy 3dz2 3dx2-y2 4px

4py

4pz

5s

n = 2

l = 1

ml = 0

ms = - ½

n = 3

l = 0

ml = 0

ms = +½

n = 4

l = 1

ml = 0

ms = +½

n = 3

l = 2

ml = -2

ms = -½

n = 3

l = 1

ml = +1

ms = +½

n = 2

l = 0

ml = 0

ms = - ½

n = 3

l = 1

ml = +1

ms = +½

n = 3

l = 2

ml = -1

ms = - ½

n = 4

l = 0

ml = 0

ms = +½

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 , l = 1 , ml = +1 and ms = + ½

b) a 3s2 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 (ü ) 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: What are the allowed values for l in each of the following cases?

a) n = 5 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 symbol What it Describes

1. The Principal Quantum Number (n): • the allowed values for n are 1, 2, 3 …infinity

n • describes the size of the quantum

level or how far the electrons are

from the nucleus (their energy)

2. The Orbital Shape or Angular Momentum

Quantum Number (l): • the allowed values for l are 0, 1, 2, 3 … (n – 1)

l • the shape of the energy sub-levels

(types of orbitals) within each

principal quantum level

3. The Magnetic Quantum Number (ml):

• the allowed values for ml are – l …. + l

ml • indicates the three dimensional

orientation of an electron

Question 3:

n l ml

n = 4 0

1

2

3

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. On the Periodic Table below, label the:

a) Group numbers and Periods

b) s,p,d and f blocks of elements

c) the transition elements and inner-transition elements

d) Noble gases, Alkali metals, Alkaline Earth metals, and Halogens

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1s1 1s

2

2s1 2s

2 2p

1 2p

2 2p

3 2p

4 2p

5 2p

6

3s1 3s

2 Transition Elements (d block) 3p

1 3p

2 3p

3 3p

4 3p

5 3p

6

4s1 4s

2 3d

1 3d

2 3d

3 3d

4 3d

5 3d

6 3d

7 3d

8 3d

9 3d

10 4p

1 4p

2 4p

3 4p

4 4p

5 4p

6

5s1 5s

2 4d

1 4d

2 4d

3 4d

4 4d

5 4d

6 4d

7 4d

8 4d

9 4d

10 5p

1 5p

2 5p

3 5p

4 5p

5 5p

6

6s1 6s

2 5d

1 5d

2 5d

3 5d

4 5d

5 5d

6 5d

7 5d

8 5d

9 5d

10 6p

1 6p

2 6p

3 6p

4 6p

5 6p

6

7s1 7s

2 6d

1 6d

2 6d

3 6d

4 6d

5 6d

6 6d

7 6d

8 6d

9 6d

10 7p

1 7p

2 7p

3 7p

4 7p

5 7p

6

4f1 4f

2 4f

3 4f

4 4f

5 4f

6 4f

7 4f

8 4f

9 4f

10 4f

11 4f

12 4f

13 4f

14

5f1 5f

2 5f

3 5f

4 5f

5 5f

6 5f

7 5f

8 5f

9 5f

10 5f

11 5f

12 5f

13 5f

14

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

Group→

:

Period ↓

1

2

3

4

5

6

Noble

↓ gases Halogens

↓

Alkali metals

Alkaline Earth metals

Inner Transition

Elements

(f block)