ChemTeam: Quantum Numbers (2024)

Quantum Numbers:
Only the Examples and Problems

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Fifteen Examples

Example #1: An electron cannot exist in the energy state described by which set of quantum numbers below?

(a) 3, 2, 2, −12
(b) 4, 3, 3, +12
(c) 2, 1, −3, +12
(d) 2, 0, 0, −12
(e) 1, 0, 1, −12

Example #2: Identify which sets of quantum numbers are valid for an electron. Each set is ordered (n, ℓ, m, ms)

(a) 2, 2, −1, +12(g) 2, 1, −1, +12
(b) 0, 2, 1, +12(h) 1, 2, 0, +12
(c) 2, 0, 0, −12(i) 1, 0, 0, ±12
(d) 3, −2, −1, −13(j) 4, 3, 1, −12
(e) 3, 2, 1, +12(k) 3.5, 3, 1, +12
(f) 4, 3, −5, −12(o) 3, 2, 1, −1

Example #3: Indicate which of the following quantum states are allowed and which are disallowed under the rules governing the electronic structure of atoms.

(a) n = 2, ℓ = 1, m = 0, ms = +12
(b) n = 3, ℓ = 3, m = −2, ms = −12
(c) n = 4, ℓ = 3, m = −2, ms = +12
(d) n = 3, ℓ = 2, m = 2, ms = +13
(e) n = 2, ℓ = 1, m = −2, ms = −12
(f) n = 3, ℓ = 2, m = −1, ms = −12

Example #4: Explain why each of the following sets of quantum numbers would not be permissible for an electron according to the rules for quantum numbers.

(a) n = 1, ℓ = 0, m = 0, ms = +1
(b) n = 1, ℓ = 3, m = 3, ms = +12
(c) n = 3, ℓ = 2, m = 3, ms = −12
(d) n = 0, ℓ = 1, m = 0, ms = +12
(e) n = 2, ℓ = 1, m = −1, ms = +32
(f) n = 4, ℓ = 3, m = 5, ms = +12

Example #5: A hydrogen atom has n = 5 and m = −2. What are the possible values for ℓ in this orbital?

Example #6: Which of the following is a possible set of quantum numbers in an atom?

(a) 3, 2, −1, +1
(b) 3, 3, −1, +12
(c) 3, 1, −2, −12
(d) 3, 1, 0, +12

Example #7: An orbital has n = 4 and m = −1. What are the possible values of ℓ for this orbital?

Example #8: In potassium how many electrons will have ℓ = 0 as one of its quantum numbers.

Example #9: In a single atom, what is the maximum number of electrons that can have the quantum numbers n = 4 and m = 2

Example #10: Determine which set(s) of quantum numbers is NOT allowed:

(a) n = 5, ℓ = 3, m = −1, ms = +12
(b) n = 1, ℓ = 0, m = 0, ms = −12
(c) n = 2, ℓ = 2, m = 2, ms = +12
(d) n = 4, ℓ = 1, m = 0, ms = −12
(e) n = 6, ℓ = 4, m = −3, ms = +12

Example #11: All the following sets of quantum numbers describe nonexistent orbitals. Find the mistake in each one.

(a) n = 0, ℓ = 3, m = −3, ms = +12
(b) n = 3, ℓ = −1, m = 0, ms = +12
(c) n = 3, ℓ = 2, m = −3, ms = −12
(d) n = 5, ℓ = 3, m = −2, ms = −1

Example #12: An electron in an atom is in the n = 3 and ℓ = 1 quantum state. Identify the possible values of m that it can have.

Example #13: What are all the possible values of ℓ when n = 3?

(a) ℓ = 0, 1, 2, 3

(b) ℓ = −2, −1, 0, 1, 2

(c) ℓ = −3, −2, −1, 0, 1, 2, 3

(d) ℓ = 0, 1, 2

Example #14: Which of the following combination of quantum numbers is/are allowed?

(a) n = 1, ℓ = 0, m = 0, ms = +12
(b) n = 1, ℓ = 3, m = 3, ms = +12
(c) n = 3, ℓ = 2, m = −2, ms = −12
(d) n = 2, ℓ = 1, m = −1, ms = +32

Example #15: Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom?

(a) n = 4, ℓ = 2, m = −1, ms = −12
(b) n = 6, ℓ = 2, m = 1, ms = +12
(c) n = 1, ℓ = −1, m = −2, ms = +12
(d) n = 6, ℓ = 0, m = 1, ms = +12

Bonus Example #1: Assign a correct set of four quantum numbers for the valence electron in a sodium atom.

Bonus Example #2: What are the possible values of n and m for an electron in a 5d orbital? Write the n, ℓ, m for each of the orbitals in the 5d subshell.

Probs 1-10

Problem #1: Which of the following is a possible set of quantum numbers that describes an electron?

(a) n = 3, ℓ = 2, m = −3, ms = −12 (d) n = 3, ℓ = 1, m = −1, ms = +12

(b) n = 0, ℓ = 0, m = 0, ms = +12

(e) n = 4, ℓ = −3, m = −1, ms = +1

(c) n = 4, ℓ = 2, m = −1, ms = 0

(f) none

Problem #2: Each electron orbital is characterized by 3 quantum numbers: n, ℓ, and m.

n is known as the ____ quantum number.
ℓ is known as the ____ quantum number.
m is known as the ____ quantum number.

Problem #3: Each electron orbital is characterized by 3 quantum numbers: n, ℓ, and m.

n specifies ___.
ℓ specifies ___.
m specifies ___.

(a) The subshell or orbital shape.
(b) The energy and average distance from the nucleus.
(c) The orbital orientation.

Problem #4: Give the orbital designation (1s, 2p, 3d, etc.) of electrons with the following combination of principal and azimuthal quantum numbers.

(a) n = 1, ℓ = 0
(b) n = 2, ℓ = 1
(c) n = 3, ℓ = 2
(d) n = 5, ℓ = 3
(e) n = 6, ℓ = 0
(f) n = 4, ℓ = 2

Problem #5: For the quantum number ℓ values below, how many possible values are there for the quantum number m?

(a) 5; (b) 3; (c) 2; (d) 1

Problem #6: What does a set of four quantum numbers tell you about an electron? Compare and contrast the locations and properties of two electrons with quantum number sets (4, 3, 1, +12) and (4, 3, −1, +12).

Problem #7: Identify the shell/subshell that each of the following sets of quantum numbers refers to.

(a) n = 2, ℓ = 1, m = 1, ms = +12
(b) n = 3, ℓ = 2, m = 2, ms = +12
(c) n = 4, ℓ = 1, m = −1, ms = −12
(d) n = 4, ℓ = 3, m = 3, ms = −12
(e) n = 5, ℓ = 0, m = 0, ms = +12

Problem #8: Which of the following set of quantum numbers (ordered n, ℓ, m, ms) are possible for an electron in an atom?

Select all that apply:

(a) 3, 2, 2, −12(f) 5, 3, −3, +12
(b) 2, 1, 3, +12(g) 3, 1, −2, −12
(c) −3, 2, 2, −12(h) 5, 3, 0, +12
(d) 3, 3, 1, −12(i) 3, 2, −1, ±12
(e) 3, 2, 1, −1(j) 3, 2, −1, 0

Problem #9: For principal quantum number n = 4, the total number of orbitals having ℓ = 3 is?

Problem #10: The maximum number of electrons that can have principal quantum number n = 3 and spin −12 is?

Bonus Problem #1: Give the maximum number of electrons in an atom that can have these quantum numbers:

(a) n = 4
(b) n = 5, m = +1
(c) n = 5, ms = +12
(d) n = 3, ℓ = 2
(e) n = 1, ℓ = 0, m = 0

Bonus Problem #2: What is the Principal Quantum Number of the first shell to have:

(a) s orbitals?
(b) p orbitals?
(c) d orbitals?
(d) f orbitals?

Probs 11-25

Problem #11: What is the maximum number of electrons that can be identified with the following set of quantum numbers?

(a) n = 4, ℓ = 0, m = 0, ms = +12
(b) n = 3, m = +2, ms = +12
(c) n = 3, m = 0, ms = +12

Problem #12: What is the maximum number of electrons that can have the following sets of quantum numbers?

(a) n = 4, ℓ = 3, m = 3, ms = −12
(b) n = 4, ℓ = 3, m = 4, ms = −12

Problem #13: In an atom, what is the maximum number of electrons that can have the following quantum numbers?

(a) n = 6, ℓ = 4
(b) n = 6, ℓ = 4, m = −1

Problem #14: Which of the following combinations of quantum numbers are allowed?

(a) n = 1, ℓ = 1, m = 0
(b) n = 3, ℓ = 0, m = 0
(c) n = 1, ℓ = 0, m = −1
(d) n = 2, ℓ = 1, m = 2

Problem #15: The following sets of quantum numbers, listed in the order n, ℓ, m, and ms were written for the last electron added to an atom. Identify which sets are valid:

nmms
I.210+12
II.22-1+12
III.20112
IV.422+12

Which of the following sets of quantum numbers is/are allowed?

(a) I and III
(b) I and IV
(c) I, II, and III
(d) II, III, and IV
(e) They are all allowed.

Problem #16: Which of the following quantum number cannot be the same for an electron in the 2p orbital and one in the 3d orbital?

I. n
II. ℓ
III. m
IV. ms
(a) I only
(b) I and II only
(c) I, II, III
(d) I, II, IV
(e) I, II, III, IV

Problem #17: Which of the following is not a valid set of four quantum numbers? (Order ---> n, ℓ, m, ms) Why?

(a) 2, 1, 0, −12
(b) 3, 1, −1, −12
(c) 1, 0, 0, +12
(d) 2, 0, 0, +12
(e) 1, 1, 0, +12

Problem #18: Determine which sets of quantum numbers are correct and which are incorrect.

(a) 14, 9, −3, −12
(b) 9, 5, −1, 0
(c) 15, 2, -6, +12
(d) 7, 10, 0, +12
(e) 10, 9, 1, +34

Problem #19: Classify each set of quantum numbers as possible or not possible for an electron in an atom.

(a) 3, 2, −3, +12(e) 3, 2, 0, −2
(b) 4, 3, −2, +12(f) 4, 3, 4, −12
(c) −2, 1, 0, −12(g) 2, 1, 0, +12
(d) 2, 2, 2, +12(h) 4, 2, −2, +12

Problem #20: What is wrong with the following set of quantum numbers?

n = 2, ℓ = 2, m = 0, ms = +12

Problem #21: Give the quantum numbers for all orbitals in the 5f subshell.

Problem #22: Which of the following set of quantum numbers (ordered n, ℓ, m, ms) are possible for an electron in an atom?

(a) 3, 2, 0, −2
(b) 3, 4, 0, +12
(c) 3, 1, 0, −12
(d) 4, 2, −1, −32
(e) 2, 1, −2, +12
(f) −1, 0, 0, −12
(g) 4, 2, 1, −12
(h) 2, 1, 3, +12

Problem #23: Which set of quantum numbers cannot occur together to specify an orbital?

(a) n = 3, ℓ = 2, m = 3
(b) n = 2, ℓ =1, m = −1
(c) n = 3, ℓ = 1, m = −1
(d) n = 4, ℓ = 3, m = 3

Problem #24: Identify which sets of quantum numbers are valid for an electron. Each set is ordered (n, ℓ, m, ms)

(a) 3, 1, −1, +12(g) 4, 3, 4, −12
(b) 3, 2, −1, 0(h) 2, 1, 1, +12
(c) 3, 2, 1, +12(i) 4, 3, 1, −12
(d) 3, −2, −2, −12(j) 1, 0, 0, −12
(e) 2, 3, 1, +12(k) 2, −1, 1, −12
(f) 1, 3, 0, +12(ℓ) 0, 1, 1, −12

Problem #25: Which of the following set of quantum numbers (ordered n, ℓ, m, ms) are possible for an electron in an atom?

(a) 4, 3, 4, −12(e) 3, 2, −3, +12
(b) 2, 1, 0, +12(f) 2, 2, 2, +12
(c) −2, 1, 0, −12(g) 3, 2, 1, −1
(d) 5, 3, −3, +12(h) 4, −2, 1, −12

Problem #26: Determine the number of electrons that can be described by each of the given quantum numbers:

(a) n = 3, ℓ = 2
(b) n = 3, ℓ = 3, m = +1
(c) n = 4
(d) n = 4, ℓ = 3, m = +1, ms = +12
(e) n = 2, ℓ = 2, m = 2, ms = −12

Bonus Problem #1: All of the following sets of quantum numbers (ordered n, ℓ, m, ms) are not possible for an electron in an atom. Identify the error in each one.

(a) 0, 0, 0, 12 (e) −4, 3, 1, 12
(b) 2, 1, 0, −1 (f) 3, 2, 2, 13
(c) 5, 3, 4, 12 (g) 3, 1, 2, −12
(d) 3.5, 2, 1, −12 (h) 3, 2, −3, 12

Bonus Problem #2: One QN in each set is not allowed. Identify the mistake and replace it with one that is allowed.

(a) n = 3, ℓ = 3, m = +2
(b) n = 2, ℓ = 1, m = −2
(c) n = 1, ℓ = 1, m = 0

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ChemTeam: Quantum Numbers (2024)

FAQs

ChemTeam: Quantum Numbers? ›

The set of quantum numbers ( n , l , m ) is forbidden are 1, 1, 0.

What is the forbidden quantum number? ›

The set of quantum numbers ( n , l , m ) is forbidden are 1, 1, 0.

What are the 4 types of quantum numbers? ›

The set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers. There are four quantum numbers, namely, principal, azimuthal, magnetic and spin quantum numbers.

What quantum numbers are permissible? ›

The principal quantum number (n) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on. The angular quantum number (l) can be any integer between 0 and n - 1. If n = 3, for example, l can be either 0, 1, or 2.

Where can I find quantum numbers? ›

The principal quantum number can be determined by looking at the period (numbered row) of the element on the periodic table. The principal quantum numbers of electrons in the S-block and P-block are the same as the period number.

What is strange quantum number? ›

The strangeness quantum number specifies the number of strange quarks present in a particle. It is a conserved quantity in strong and electromagnetic interactions, but can change under weak interactions. A particle having one strange quark has an of -1, while one with a strange antiquark has an of +1.

What is a bad quantum number? ›

A set of eigenvalues from a complete commuting set of operators are called good quantum numbers. The eigenvalues from a non-commuting operator are a bad quantum numbers, because their values cannot be known simultaneously. This is not quite as simple as it seems.

What is the n/l rule? ›

The (n+l) rule, also known as the Aufbau principle or Aufbau sequence, determines the energy of all atomic orbitals. The rule says that the orbital having a lower value of (n+l) is filled first. If two orbitals have the same n+l, the one with lower n is filled first. The first orbital we fill in is the 1s orbital.

Can all 4 quantum numbers be the same? ›

All the four quantum number can never be same for any two electrons. Heisenberg Uncertainty principle. Pauli Exclusion Principle.

What could be the fourth quantum number? ›

The fourth quantum number is the spin quantum number. Each electron has a spin quantum number, ms, that can be equal to ±½. No two electrons in the same atom can have the same set of values for all the four quantum numbers, known as the Pauli exclusion principle.

What is the most important quantum number? ›

The Principal Quantum Number (n)

Because n describes the most probable distance of the electrons from the nucleus, the larger the number n is, the farther the electron is from the nucleus, the larger the size of the orbital, and the larger the atom is.

Who is the father of quantum number? ›

Answer and Explanation:

Niels Bohr introduced in 1913 the principal quantum number (n) in order to better interpret the concept of the orbitals.

What quantum numbers are invalid? ›

Flexi Says: An example of an invalid set of quantum numbers could be (n = 2, l = 2, m = 0, s = +1/2). This set is invalid because the value of the quantum number "l" (angular momentum) is not allowed to equal or exceed the value of "n" (principal quantum number).

Which quantum number determines what? ›

Detailed Solution
Spin quantum numberDetermines the orientation of the spin axis of an electron.
Principal quantum numberDetermines the energy of an electron and the size of the orbital.
Magnetic quantum numberDetermines the number of orbitals and their orientation within a subshell.

What is the L in quantum numbers? ›

Angular Momentum Quantum Number (l)

The angular momentum quantum number, signified by l, describes the general shape or region an electron occupies—its orbital shape. The value of l depends on the value of the principal quantum number, n. The angular momentum quantum number can have positive values of zero to (n−1).

What are the quantum numbers of oxygen? ›

For 8th electron of oxygen atom, the four quantum numbers are n=2,l=1,m=+1 or −1,s=+12 or −12. Was this answer helpful?

Which of the quantum numbers are not allowed? ›

The set of quantum numbers n=1,l=1,ml=0,ms=+12 is not possible for an electron.

What quantum numbers Cannot exist? ›

The value of spin quantum number can never be a zero, because electrons always have spin either positive or negative. Hence, n = 1, l = 0, ml = 0, ms = 0, this set of quantum number is not possible.

What is an invalid quantum number? ›

Flexi Says: An example of an invalid set of quantum numbers could be (n = 2, l = 2, m = 0, s = +1/2). This set is invalid because the value of the quantum number "l" (angular momentum) is not allowed to equal or exceed the value of "n" (principal quantum number).

What is forbidden in quantum mechanics? ›

Transitions between energy levels in a quantum-mechanical system that are not allowed to take place because of selection rules. In practice, forbidden transitions can occur, but they do so with much lower probability than allowed transitions.

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