3.1.1.0: Atomic Orbitals and Quantum Numbers (Problems)
PROBLEM \(\PageIndex{1}\)
What are the allowed values for each of the four quantum numbers: n , l , m l , and m s ?
- Answer
-
n: non-zero integer
l: 0 to n-1
m l : -l to l
m s : \(\dfrac{1}{2}\) or \(\dfrac{-1}{2}\)
PROBLEM \(\PageIndex{2}\)
Describe the properties of an electron associated with each of the following four quantum numbers: n , l , m l , and m s .
- Answer
-
n determines the general range for the value of energy and the probable distances that the electron can be from the nucleus. l determines the shape of the orbital. m l determines the orientation of the orbitals of the same l value with respect to one another. m s determines the spin of an electron
PROBLEM \(\PageIndex{3}\)
Identify the subshell in which electrons with the following quantum numbers are found:
- n = 2, l = 1
- n = 4, l = 2
- n = 6, l = 0
- Answer a
-
2p
- Answer b
-
4d
- Answer c
-
6s
PROBLEM \(\PageIndex{4}\)
Identify the subshell in which electrons with the following quantum numbers are found:
- n = 3, l = 2
- n = 1, l = 0
- n = 4, l = 3
- Answer a
-
3d
- Answer b
-
1s
- Answer c
-
4f
PROBLEM \(\PageIndex{5}\)
Consider the orbitals shown here in outline.
- What is the maximum number of electrons contained in an orbital of type (x)? Of type (y)? Of type (z)?
- How many orbitals of type (x) are found in a shell with n = 2? How many of type (y)? How many of type (z)?
- Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n = 4. Of an orbital of type (y) in a shell with n = 2. Of an orbital of type (z) in a shell with n = 3.
- What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)?
- What are the possible l and m l values for an orbital of type (x)? Of type (y)? Of type (z)?
- Answer a
-
x. 2
y. 2
z. 2
- Answer b
-
x. 1
y. 3
z. 0
- Answer c
-
x. 4 0 0 \(\dfrac{1}{2}\)
y. 2 1 0 \(\dfrac{1}{2}\)
z. 3 2 0 \(\dfrac{1}{2}\)
- Answer d
-
x. 1
y. 2
z. 3
- Answer e
-
x. l = 0, m l = 0
y. l = 1, m l = –1, 0, or + 1
z. l = 2, m l = –2, –1, 0, +1, +2
PROBLEM \(\PageIndex{6}\)
How many electrons could be held in the second shell of an atom if the spin quantum number m s could have three values instead of just two? (Hint: Consider the Pauli exclusion principle.)
- Answer
-
12
PROBLEM \(\PageIndex{7}\)
Write a set of quantum numbers for each of the electrons with an n of 4 in a Se atom.
- Answer
-
n l m l s 4 0 0 \(+\dfrac{1}{2}\) 4 0 0 \(−\dfrac{1}{2}\) 4 1 −1 \(+\dfrac{1}{2}\) 4 1 0 \(+\dfrac{1}{2}\) 4 1 +1 \(+\dfrac{1}{2}\) 4 1 −1 \(−\dfrac{1}{2}\)
PROBLEM \(\PageIndex{8}\)
Answer the following questions:
- Without using quantum numbers, describe the differences between the shells, subshells, and orbitals of an atom.
- How do the quantum numbers of the shells, subshells, and orbitals of an atom differ?
- Answer a
-
shell: set of orbitals in the same energy level
subshell: set of orbitals in the same energy level and same shape (s, p, d, or f)
orbital: can hold up to 2 electrons
- Answer b
-
shell: set of orbitals with same n
subshell: set of orbitals in an atom with the same values of n and l
orbital: shape defined by l quantum number
PROBLEM \(\PageIndex{9}\)
Sketch the boundary surface of a p z and a p y orbital. Be sure to show and label the axes.
- Answer
-
PROBLEM \(\PageIndex{10}\)
Sketch the p x and s orbitals. Be sure to show and label the coordinates.
- Answer
-
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Contributors and Attributions
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110 ).
- Adelaide Clark, Oregon Institute of Technology