Questions About Quantum Numbers

Questions About Quantum Numbers

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 Multiple-Choice Questions: Quantum Numbers

1. What does the principal quantum number (n) determine?
   A) Shape of the orbital
   B) Orientation of the orbital
   C) Spin of the electron
   D) Main energy level of the electron
   E) Type of chemical bond

2. Which quantum number determines the shape of an orbital?
   A) Principal quantum number (n)
   B) Magnetic quantum number (mₗ)
   C) Azimuthal (angular momentum) quantum number (ℓ)
   D) Spin quantum number (ms)
   E) Electric quantum number

3. The magnetic quantum number (mₗ) specifies:
   A) Size of the atom
   B) Orientation of the orbital in space
   C) Shape of the orbital
   D) Number of electrons in an orbital
   E) Energy level of the electron

4. The spin quantum number (ms) can have which values?
   A) 0 or 1
   B) −2 or +2
   C) −1 or +1
   D) +½ or −½
   E) Any integer

5. What is the maximum number of electrons in an orbital?
   A) 1 B) 2 C) 4 D) 6 E) Infinite

6. If n = 3, what are the possible values of ℓ?
   A) 0, 1 B) 0, 1, 2 C) 1, 2, 3< D) 0, 1, 2, 3 E) Only 3

7. If ℓ = 2, what type of orbital is it?
   A) s B) p C) d D) f E) g

8. What is the total number of orbitals in the n = 2 level?
   A) 2 B) 4 C) 3 D) 6 E) 5

9. Which quantum number is the same for all electrons in the same shell?
   A) ℓ B) ms C) n D) mₗ E) None

10. What is the shape of orbitals with ℓ = 1?
    A) Spherical B) Dumbbell C) Cloverleaf D) Ring E) Spiral

11. How many orbitals are in a d subshell?
    A) 3 B) 5 C) 7 D) 9 E) 10

12. How many electrons can occupy the n = 4 level?
    A) 16 B) 8 C) 32 D) 18 E) 10

13. What is the maximum number of electrons in a p subshell?
    A) 2 B) 4 C) 6 D) 8 E) 10

14. If an electron has quantum numbers n = 2, ℓ = 1, mₗ = 0, ms = +½, what orbital is it in?
    A) 2s B) 2p₀ C) 3p D) 1s E) 2d

15. Which set of quantum numbers is not allowed?
    A) n = 2, ℓ = 0, mₗ = 0, ms = −½ B) n = 3, ℓ = 2, mₗ = 2, ms = +½ C) n = 1, ℓ = 0, mₗ = 0, ms = +½ D) n = 4, ℓ = 3, mₗ = −3, ms = −½ E) n = 2, ℓ = 2, mₗ = 0, ms = +½

16. Which subshell corresponds to n = 4 and ℓ = 3?
    A) 4s B) 4p C) 4d D) 4f E) 4g

17. What does the Pauli Exclusion Principle state about quantum numbers?
    A) Electrons must fill lower energy levels first
    B) Electrons must occupy separate orbitals
    C) No two electrons can have the same four quantum numbers
    D) Orbitals must be filled singly before pairing
    E) Electrons always spin in opposite directions

18. Which principle states that electrons fill orbitals starting with the lowest energy levels first?
    A) Pauli Exclusion Principle
    B) Heisenberg Principle
    C) Aufbau Principle
    D) Hund’s Rule
    E) Schrödinger Principle

19. Which rule explains why electrons occupy orbitals singly before pairing up?
    A) Pauli Exclusion Principle
    B) Hund’s Rule
    C) Aufbau Principle
    D) Bohr’s Rule
    E) Rutherford’s Rule

20. How many total quantum numbers are used to describe an electron in an atom?
    A) 2
    B) 3
    C) 4
    D) 5
    E) 6

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• Questions on Quantum Mechanics
• Questions on Heisenberg Uncertainty Principle
• Questions About Energy Levels

Answers and Explanations

1. D – Main energy level of the electron
   The principal quantum number (n) defines the shell/energy level.

2. C – Azimuthal (angular momentum) quantum number (ℓ)
   ℓ defines the shape: s, p, d, f.

3. B – Orientation of the orbital in space
   mₗ determines the spatial orientation of orbitals.

4. D – +½ or −½
   Electrons can spin up or down, corresponding to these values.

5. B – 2
   Each orbital can hold a maximum of two electrons with opposite spins.

6. B – 0, 1, 2
   ℓ ranges from 0 to (n − 1). For n = 3, ℓ = 0, 1, 2.

7. C – d
   ℓ = 2 corresponds to the d subshell.

8. B – 4
   For n = 2, ℓ = 0 (1 orbital) and ℓ = 1 (3 orbitals): total = 4.

9. C – n
   All electrons in the same shell share the same principal quantum number.

10. B – Dumbbell
    p orbitals (ℓ = 1) have a dumbbell shape.

11. B – 5
    d subshells have 5 orbitals (mₗ = −2 to +2).

12. C – 32
    Maximum electrons = 2n² = 2×16 = 32.

13. C – 6
    p subshell: 3 orbitals × 2 electrons = 6.

14. B – 2p₀
    ℓ = 1 → p; mₗ = 0 indicates the central p orbital.

15. E – n = 2, ℓ = 2, mₗ = 0, ms = +½
    ℓ must be less than n. ℓ = 2 is invalid for n = 2.

16. D – 4f
    ℓ = 3 corresponds to the f subshell.

17. C – No two electrons can have the same four quantum numbers
    This is the Pauli Exclusion Principle.

18. C – Aufbau Principle
    Electrons fill from lower to higher energy orbitals.

19. B – Hund’s Rule
    Electrons fill orbitals singly first, with parallel spins.

20. C – 4
    Each electron is defined by n, ℓ, mₗ, and ms.

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Ronaldo Silva: Professor and Specialist in Science Teaching, from UFF/RJ, with more than 25 years of experience in teaching.