The fourth quantum number, m_{s}, determines the spin of an electron within an atomic orbital.

Whereas the first 3 quantum numbers describe the atomic orbital where you find the electron, the final quantum number, m_{s}, describes spin the electron possesses.

**Concept:** Spin Quantum Number Part 1

The **Pauli Exclusion Principle** implies that two electrons in the same atomic orbital cannot spin in the same direction so as to avoid having the same four quantum numbers.

**Concept:** Spin Quantum Number Part 2

**Example:** State the electron configuration of boron and list the four quantum numbers of the 1** ^{st}** and the 5

Write a full set of quantum numbers for the following:

(a) The outermost electron in an Li atom

(b) The electron gained when a Br atom becomes a Br– ion

(c) The electron lost when a Cs atom ionizes

(d) The highest energy electron in the ground-state B atom

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Write a full set of quantum numbers for the following:

(a) The outermost electron in an Rb atom

(b) The electron gained when an S– ion becomes an S2– ion

(c) The electron lost when an Ag atom ionizes

(d) The electron gained when an F– ion forms from an F atom.

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Which of the quantum numbers relate(s) to the electron only? Which relate(s) to the orbital?

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Which of the following set of quantum numbers (ordered n,l,ml,ms) are possible for an electron in an atom? Check all that apply.

a. 3, 4, 0, 1/2

b. 3, 2, 0, -1/2

c. 3, 2, 2, -1/2

d. 3, 1, 0, -1/2

e. -3, 2, 2, -1/2

f. 4, 3, 4, -1/2

g. 2, 1, 0, 1

h. 2, 1, -2, 1/2

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Which of the following set of quantum numbers (ordered n, ℓ, m _{ℓ}, m_{s}) are possible for an electron in an atom? Check all that apply.

a. 5, 3, 0, 1/2

b. 2, 1, 0, 1/2

c. 3, 1, 0, -1/2

d. 2, 1, 0, 1

e. 2, 1, -2, 1/2

f. 3, 4, 0, 1/2

g. 5, 3, 4, 1/2

h. -1, 0, 0, -1/2

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**Part A**

What is the only possible value of *m*_{l} for an electron in an *s* orbital?

Express your answer numerically.

**Part B**

What are the possible values of m _{l} for an electron in a *d* orbital?

Express your answer numerically with sequential values separated by commas.

**Part C**

Which of the following set of quantum numbers (ordered *n*, l, *m *_{l}, *m*s) are possible for an electron in an atom?

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For an electron that has quantum numbers n = 3 and m _{l} = 2, which of the following is true?

A. it must have the quantum number m _{s} = + 2

B. it must have the quantum number *l* = 1

C. it may have the quantum numbers, *l* = 0, 1, 2

D. it must have the quantum number *l* = 2

E. none of these answers apply to this electron

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Which of the following is a possible set of quantum numbers?

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Which of the following is not a permitted combination of quantum numbers?

1. n = 4, ℓ = 2, mℓ = 1, m _{s} = 1/2

2. n = 3, ℓ = 0, mℓ = 0, m _{s} = 1/2

3. n = 4, ℓ = 3, mℓ = 3, m _{s} = − 1/2

4. n = 2, ℓ = 1, mℓ = −2, m _{s }= 1/2

5. n = 3, ℓ = 0, mℓ = 0, m _{s} = − 1/2

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What is the smallest acceptable value for the missing quantum number?

*n* = ?, ℓ = 2, *m*_{ℓ} = 0, *m _{s}* = +1/2

A) 4

B) 3

C) 1

D) 5

E) 2

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Which of the following represents a set of quantum number for valence electron of Chlorine?

A. (3,1,0,-1)

B. (3, 2, 0, -1/2)

C. (3,0,2, 1/2)

D. (3,1,-1, -1/2)

E. (3,1,0,0)

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Each of the following sets of quantum numbers gives information on a specific orbital. Find the error in each.

a) n = 4, l = 0 , m _{l} = 1, m _{s} = -1/2

b) n = 5, l = 2 , m _{l} = - 1, m _{s} = 1

c) n = 7, l = 7, m _{l} = - 5, m _{s} = -1/2

d) n = 22, l = 5, m _{l} = - 6, m _{s} = 1/2

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How many electrons can have the following quantum sets?

a. In the 7 ^{th} shell of an atom (n = 7)

b. n = 5, ℓ = 2

c. n = 6, ℓ = 3, m _{ℓ} = -2

d. n = 4, ℓ = 2, m _{ℓ} = 0 , m _{s} = -1/2

e. n = 4, m _{ℓ} = -1

f. n = 5, m _{ℓ} = 0 , m _{s} = 1/2

g. n = 9, ℓ = 4, m _{s} = -1/2

h. n = 2, m _{s} = 1/2

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Which set of quantum numbers is correct and consistent with n = 4?

(A)* l* = 3 m _{l }= -3 m_{s} = +1/2

(B)* l *= 4 m _{l }= +2 m_{s }= -1/2

(C) *l* = 2 m _{l }= +3 m_{s} = +1/2

(D)* l* = 3 m _{l} = -3 m_{s} = +1

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Which set of quantum numbers is *not *possible?

a) *n* = 2, *l* = 1, m _{l}, = +1, m _{s} = –1/2

b) *n* = 3, *l* = 2, m _{l} = +1, m _{s} = +1/2

c) *n* = 4, *l* = 4, m _{l} = –1, m _{s} = +1/2

d) *n* = 5, *l* = 2, m _{l} = 2, m _{s} = –1/2

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Which of the following sets of the four quantum numbers n, l, m _{l}, and m_{s} decribes one of the outermost electrons in a ground-state barium atom?

a) 6, 1, 1, ½

b) 6, 0, 1, -½

c) 6, 0, 0, -½

d) 6, 1, 0, ½

e) 6, 2, 1, -½

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Which of the following set is an acceptable set of quantum numbers?

a. n = 0, l = 0, m _{l} = 0, m _{s} = +1/2

b. n = 2, l = 1, m _{l} = 2, m _{s} = −1/2

c. n = 2, l = 0, m _{l} = 0, m _{s} = 1

d. n = 1, l = 1, m _{l} = 0, m _{s} = −1/2

e. n = 3, l = 1, m _{l} = −1, m _{s} = −1/2

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How many electrons can have the following quantum numbers

a) n=3, l=1, m_{s}=1/2

b) n=4, m _{l} = -1

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Which of the following is a possible set of quantum numbers for a 3d electron?

a) n=4, l=3, m _{l}=2, m_{s}=-1/2

b) n=3, l=2, m _{l}=0, m_{s}=-1/2

c) n=3, l=1, m _{l}=1, m_{s}=+1/2

d) n=3, l=3, m _{l}=2, m_{s}=+1/2

e) n=3, l=0, m _{l}=0, m_{s}=+1/2

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Which one of the following represents a 2p electron in an atom?

a. 2, 1, -1, +1/2

b. 2, 1, 0, 0

c. 2, 2, 0, -1/2

d. 2, 0, 1, -1/2

e. 2, 0, 2, +1/2

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Which of the following represents an impossible set of quantum numbers for an electron in an atom?

a. 2, 1, -1, -1/2

b. 1, 0, 0, +1/2

c. 3, 3, 3, +1/2

d. 5, 4, -3, +1/2

e. 5, 4, -3, -1/2

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For an electron that has quantum numbers n = 3 and m _{l} = 2, which of the following is true?

A) it must have the quantum number m _{s} = + 1/2

B) it must have the quantum number* l *= 1

C) it may have the quantum numbers, *l* = 0, 1, 2

D) it must have the quantum number *l* = 2

E) none of these answers apply to this electron

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Fluorine can gain an electron to become fluoride (F^{−}). What is the quantum number (following the numbering conventions) that describes the electron that was gained by fluorine.

(a) n = 2, ℓ = 0, m _{ℓ} = 1, m_{s} = -1⁄2

(b) n = 2, ℓ = 1, m _{ℓ} = 0, m_{s} = -1⁄2

(c) n = 3, ℓ = 1, m _{ℓ} = 1, m_{s} = +1⁄2

(d) n = 2, ℓ = 1, m _{ℓ} = 1, m_{s} = -1⁄2

(e) n = 2, ℓ = 1, m _{ℓ} = -1, m_{s} = -1⁄2

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The four quantum numbers (n, ℓ, m_{ℓ} , m_{s}) for the last two electrons added to complete the electron configuration if Si are:

a. (2,1,-1,½) and (2,1,0,½)

b. (3,1,-1,½) and (3,1,0,½)

c. (3,0,-1,½) and (3,1,0,½)

d. (3,2,-2,½) and (3,2,-1,-½)

e. (2,0,0,½) and (2,0,0,-½)

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Which one of the following statements is false?

a. If an electron quantum number *n*=2, it may be a *p* sublevel.

b. If an electron has ℓ=1, it must be in a *p* sublevel.

c. Two electrons in the same atom may have quantum numbers, *n* ,* l* , *m*ℓ , *m*_{s} of 2,1,-1,½, and 2,-1,- 1,½.

d. Two electrons in the same atom may **not** have quantum numbers of 2,1,-1,-½ and 2,1,-1,-½.

e. If an electron has *n*=1, it must be in an *s* orbital

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How many of the following statements are false?

I. The principal quantum number n is related to the size of an orbital.

II. *s, p, d, f* represent orbitals with different azimuthal quantum numbers.

III. The magnetic quantum number can have values of +½ or -½.

IV. The spin quantum number is related to the orientation of an orbital.

V. The electron density at a point is proportional to Ψ ^{2} at that point.

A. 0

B. 1

C. 2

D. 3

E. 4

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