Explanation:
A d-subshell has azimuthal quantum number l = 2. Therefore, m_l can take the five values from -2 to +2, corresponding to five distinct orbitals.
2. An electron is described as belonging to a 4d subshell. Which statement about its quantum numbers is necessarily correct?
A.
n = 4, l = 2, and m_l can have five possible values
B.
n = 4, l = 3, and m_l can have seven possible values
C.
n = 2, l = 4, and m_l can have nine possible values
D.
n = 4, l = 1, and m_l can have three possible values
Correct Answer:
n = 4, l = 2, and m_l can have five possible values
Explanation:
The designation 4d fixes n = 4 and identifies the d-subshell, for which l = 2. Thus, five magnetic quantum numbers and five orbitals are possible.
3. What is the maximum number of electrons that can occupy a single d-subshell, and why?
A.
2, because a d-subshell contains one orbital
B.
6, because a d-subshell contains three orbitals
C.
10, because a d-subshell contains five orbitals, each holding two electrons
D.
14, because a d-subshell contains seven orbitals
Correct Answer:
10, because a d-subshell contains five orbitals, each holding two electrons
Explanation:
For a d-subshell, l = 2, giving 2l + 1 = 5 orbitals. Since each orbital can contain two electrons with opposite spins, the maximum occupancy is 10 electrons.
4. Which set contains only valid orbitals belonging to the same d-subshell?
Explanation:
The five orbitals of a d-subshell are conventionally represented as d_xy, d_xz, d_yz, d_x2-y2, and d_z2. All five listed orbitals in the correct option have the same principal shell and d-subshell designation.
5. For an electron in a 3d subshell, what is the number of angular nodes and radial nodes, respectively?
A.
2 and 0
B.
0 and 2
C.
2 and 1
D.
1 and 2
Correct Answer:
2 and 0
Explanation:
For a d-subshell, l = 2, so the number of angular nodes is 2. The number of radial nodes is n - l - 1 = 3 - 2 - 1 = 0.
6. Which statement correctly distinguishes the angular nodal characteristics of a d orbital from those of a p orbital?
A.
A d orbital has two angular nodes, whereas a p orbital has one
B.
A d orbital has one angular node, whereas a p orbital has two
C.
Both d and p orbitals have no angular nodes
D.
Both d and p orbitals always have two angular nodes
Correct Answer:
A d orbital has two angular nodes, whereas a p orbital has one
Explanation:
The number of angular nodes equals l. For a d orbital, l = 2, giving two angular nodes; for a p orbital, l = 1, giving one angular node.
7. Which statement about the five orbitals within an isolated d-subshell is most accurate?
A.
They have different principal quantum numbers but identical orientations
B.
They have the same n and l values but differ in their allowed m_l values and spatial orientations
C.
They have different l values and therefore different subshell identities
D.
They differ only in the number of electrons they can accommodate
Correct Answer:
They have the same n and l values but differ in their allowed m_l values and spatial orientations
Explanation:
Orbitals within one d-subshell share the same n and l values. Their different m_l values correspond to different orientations of the d-orbital wavefunctions in space.
8. Which pair of quantum-number descriptions represents two different orbitals of the same 5d subshell?
Explanation:
Two orbitals belong to the same 5d subshell when n = 5 and l = 2 for both, while their allowed m_l values are different. For a d-subshell, -2 ≤ m_l ≤ +2, so both -1 and +2 are valid.
9. A subshell contains exactly five orbitals and has two angular nodes in each orbital. Which identification is correct?
A.
It is an s-subshell with l = 0
B.
It is a p-subshell with l = 1
C.
It is a d-subshell with l = 2
D.
It is an f-subshell with l = 3
Correct Answer:
It is a d-subshell with l = 2
Explanation:
Two angular nodes indicate l = 2, which defines a d-subshell. The number of orbitals is 2l + 1 = 5, confirming the identification.
10. For a 4d orbital, which combination gives its total number of nodes, angular nodes, and radial nodes, respectively?
A.
4, 2, 2
B.
3, 2, 1
C.
3, 1, 2
D.
2, 2, 1
Correct Answer:
3, 2, 1
Explanation:
For a 4d orbital, n = 4 and l = 2. Total nodes equal n - 1 = 3, angular nodes equal l = 2, and radial nodes equal n - l - 1 = 1.
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d-Subshell Characteristics
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