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Wize University Chemistry Textbook > Quantum Numbers and Electron Configurations

The Quantum Model & Orbitals

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Quantum Numbers

Quantum numbers describe where electrons are positioned around atoms:

LetterQuantum NumberDescriptionnPrincipalSizelOrbital Angular MomentumShapemlMagneticOrientationmsElectronic SpinElectron Up or Down\begin{array}{ccccc} \hline \text{Letter}&&\text{Quantum Number}&&\text{Description}\\ \hline n&&\text{Principal}&&\text{Size}\\\\ l&&\text{Orbital Angular Momentum}&&\text{Shape}\\\\ m_l&&\text{Magnetic}&&\text{Orientation}\\\\ m_s&&\text{Electronic Spin}&&\text{Electron Up or Down}\\ \hline \end{array}

Rules:
nn
  • Can be any positive integer Example: n = (1, 2, 3, 4…)
  • As n increases, energy and size of shell
    increases
Wize Tip
n is also called the "principle quantum number"


Photo by Greg Robson / CC BY
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ll
  • Can be any non-negative integer up to n-1 Example: l = (0, 1, 2, 3, …, n-1)
  • l (orbital shapes) are described as:
Increasing energy →


  • These shapes show us where an electron is most likely to be found
  • There is a 90% chance in finding an electron somewhere inside the given shape
Wize Concept
S orbitals are spheres and with increasing "n" the sphere will get larger.
There is one s orbital in a subshell.

P subshells are dumbbell shaped.
There are three p orbitals in a subshell, each orientated along an axis (px, py and pz)

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mlm_l
  • Can be any integer from –l to +l Example: m1 = (-l, …, 0, …, l)
  • This quantum # designates a specific orbital within a given shell Example: if n=2 and l=1, we are looking at 2p.
  • ml can be -1, 0, or +1 this designates each of the 2p orbitals: 2px, 2py, and 2pz


msm_s
  • Spin of an electron
  • Can only be +1/2 or -1/2

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Quantum Numbers Summary



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Example: Allowed Quantum Numbers

What are the allowed set of quantum numbers for the following orbitals?

a) 6s

n = 6
l = 0
ml = 0
ms= +1/2 or -1/2


b) 4p

n = 4
l = 1
ml = -1, 0, or 1
ms= +1/2 or -1/2


c) 3d

n = 3
l = 2
ml = -2, -1, 0, 1, or 2
ms= +1/2 or -1/2


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Example: Allowed Sets of Quantum Numbers

Which of the following sets of quantum numbers (nn, ll, mlm_l, msm_s) are allowed and which are not allowed? For the sets of quantum orbitals that are not allowed, state why it is not allowed.

(i) (4, 0, 0, 0)

Not allowed - msm_s cannot be equal to 0. Quantum number msm_s is always either +1/2 or -1/2.


(ii) (3, 1, 2, -1/2)

Not allowed - mlm_l cannot be equal to 2 if ll = 1. Remember that mlm_l equals all integers from+l+l to −l-l.


(iii) (5, 3, 0, +1/2)

Allowed. This set of quantum numbers describes a 5f orbital.


(iv) (4, 4, 3, -1/2)

Not allowed - ll cannot be equal to 4 if nn = 4. Remember that ll equals all integers from 0 to n−1n-1.


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Example: Defining Orbitals from Quantum Numbers

Determine the atomic orbital described by the following sets of quantum numbers (nn, ll, mlm_l, msm_s).

(i) (2, 0, 0, -1/2)

2s orbital

(ii) (4, 3, 0, +1/2)

4f orbital

(iII) (5, 1, 1, -1/2)

5p orbital

Practice: Valid Quantum Numbers

Determine which of the following sets of quantum numbers (n, l, ml, msn,\ l,\ m_l,\ m_s) is valid for a 3d orbital.
Extra Practice
Quantum model: Orbitals
Select the true statement.
Atomic Orbitals
How many different atomic orbitals exist where n = 3?
Quantum Numbers
How many electrons can have the following quantum numbers:
a. n = 4
b. n = 4, ms = + 1/2
Quantum Numbers
If an electron of H atom is present in the 5f orbital, what are the possible quantum numbers?
Quantum numbers
Which of the following combinations does not denote an orbital?
a. n = 2, l = 1, ml = −1
b. n = 3, l = 3, ml = 2
Quantum numbers
How many electrons can have the following quantum numbers:
a. n = 4
b. n = 4, ms = + 1/2
Orbitals
What orbitals do these following sets of quantum numbers denote?
a. n = 4, l = 3
b. n = 3, l = 0
Electronic Configuration
How many electrons in Cr+ satisfy the following condition:
a. l = 1, ms = +1/2
b. l = 2, ms = ± 1/2
Quantum Numbers
Which of the following combinations is correct?
a. n = 3, l = 2, ml = −3
b. n = 3, l = 1, ml = −2
Quantum Model: Quantum Numbers
Determine which of the following sets of quantum numbers (n, l, ml, msn,\ l,\ m_l,\ m_s) is valid for a 3d orbital.
Quantum model: Orbitals
Give quantum numbers which describe the following. Note there may be more than one correct answer
A 32g orbital
Practice: Quantum Numbers
If an electron of H atom is present in the following orbitals, what are the possible quantum numbers in each case?
a. 2p
b. 3s
Quantum Numbers
Which of the following is an allowed set of quantum numbers for a 4p orbital?
Quantum Numbers
Which atomic orbital is described by each set of quantum numbers (n, l, ml)\left(n,\ l,\ m_l\right) below?
a) (3, 2, −1)\left(3,\ 2,\ -1\right)
b) (3, 1, 0)\left(3,\ 1,\ 0\right)
CHEM 1011 (Dalhousie) - Quantum Numbers
Answer the following questions on quantum numbers.
a) Give a possible value for each quantum number for a 4d orbital.
b) (4, 1, 0, -1/2) is valid for a 4p orbital.
Quantum Numbers
10. Select all sets of quantum numbers that are valid.
Quantum Numbers
9. Which of the following is an allowed set of quantum numbers for a 3s orbital?
Quantum Numbers
8. Which atomic orbital is described by each set of quantum numbers (n, l, ml)\left(n,\ l,\ m_l\right) below?
a) (2, 1, −1)\left(2,\ 1,\ -1\right)
b) (4, 0, 0)\left(4,\ 0,\ 0\right)
Quantum Model: Quantum Numbers
Determine which of the following sets of quantum numbers (n, l, ml, msn,\ l,\ m_l,\ m_s) is valid for a 3d orbital.
Quantum. model: Electronic Configuration
A gold (Au) atom has how many electrons with the quantum numbers n=4, ml=-3?
Quantum Model: Electronic Configuration
Krypton (Kr) atom has how many electrons with the quantum numbers n=3, l=2?
Quantum model: Orbitals
Give quantum numbers which describe the following. Note there may be more than one correct answer
an electron in a 2s orbital
Quantum Model: Orbitals
Which of the following orbital designations is not allowed:
Quantum model: Orbitals
Which of the following combinations of quantum numbers (n,ℓ,mℓ)(n, \ell, m_{\ell}) are allowed?
(4, 3, 3, 0)
(2, 1, 0, +1/2)
Quantum model: Orbitals
Give quantum numbers which describe the following. Note there may be more than one correct answer
A 6f orbital:
Quantum model: Orbitals
Which of the following gives a correct “set” of name, quantum numbers and boundary surface diagrams for a highest energy atomic orbital of a nitrogen atom.
A gold (Au) atom has how many electrons with the quantum numbers n = 4, ml = -3?
Are orbitals with n = 3, l = 1 degenerate?
Which atomic orbital is described by the quantum numbers n = 4, l = 2, ml =1?
Quantum Model: Orbitals
Are all atomic orbitals (s, p, d, f) with n = 3 degenerate?
Quantum Model: Orbitals
Which set of quantum numbers n, l, can be valid for the orbital D in the figure above?
Quantum model: Quantum Numbers
Determine the quantum numbers for the final electron of Pd.
"The Periodic Table", image retrieved from Chemistry 2e (https://d3bxy9euw4e147.cloudfront.net/oscms-prodcms/media/documents/Chemistry2e-OP_QCzV58S.pdf) by Flowers, P et al., is licensed under CC BY.
Quantum Model: Orbitals
Which atomic orbital is described by the quantum numbers n=4, l=2, ml=1?
The quantum numbers for the first electron removed from an As atom could be?
The Hydrogen Atom and Visualization of the Atomic Orbitals Questions
1) Which of the following combinations of quantum numbers (n, l, ml) is allowed
a) (12, 2, -2)
b) (3, 4, 3)
Quantum model: Orbitals
Which of the following probability plots corresponds to a 5s orbital?
a) b)
c) d)
Quantum Model: Quantum number
Which of the following is a correct quantum number combination for an electron in the highest energy subshell of Selenium?
Atomic Orbitals
How many different atomic orbitals exist where n = 3?
How many combinations of quantum numbers (n, l, ml, ms) are possible for an electron if n = 3 and ml = 1?
Quantum Model: Quantum Number
Which of the following is a valid quantum number combination for an electron in the
valence shell of Si\text{Si}?
Quantum model: Orbitals
Select the true statement.
Quantum Model: Orbital energy
The sketches below show possible orbitals for the electron in a hydrogen atom. Which orbital would have the lowest energy?
Quantum Model: Quantum Numbers
Which of the following statements is true?
Which of the following quantum number combinations are not valid? (Select all that apply)
What are the four quantum numbers associated with the final valence electron of Co?
"The Periodic Table", image retrieved from Chemistry 2e (https://d3bxy9euw4e147.cloudfront.net/oscms-prodcms/media/documents/Chemistry2e-OP_QCzV58S.pdf) by Flowers, P et al., is licensed under CC BY.
Quantum model: Orbitals
How many orbitals are there in the shell where n=3?
Which of the following combinations of quantum numbers (n,ℓ,mℓ)(n, \ell, m_{\ell}) are allowed? (Select all that apply)
Quantum Model: Quantum Numbers
Which of the following describes a correct set of quantum number for an orbital?
Quantum Model: Quantum Numbers
Which quantum number describes the magnetic spin of an electron?
Periodic Table: Quantum Numbers
l = 2 refers to which block of the periodic table?