chemistry : class11 Hydrogenic Subshell Degeneracy : Concept of subshells : Structure of Atom MCQ Questions and Answers
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Hydrogenic Subshell Degeneracy
MCQ questions and answers.
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MCQ Questions
1. In a hydrogenic species, how many distinct subshells are degenerate in energy within the shell having principal quantum number n = 5?
A.
3
B.
4
C.
5
D.
25
Correct Answer:
5
Explanation:
For a hydrogenic atom, energy depends only on n, so all allowed subshells with l = 0, 1, 2, 3, 4 are degenerate. Thus, the number of degenerate subshells is n = 5.
2. Which set contains only subshells that are degenerate in a hydrogenic atom?
A.
2s, 2p, 3s
B.
3s, 3p, 3d
C.
3p, 4s, 4p
D.
4s, 4p, 5s
Correct Answer:
3s, 3p, 3d
Explanation:
In a hydrogenic atom, subshells having the same principal quantum number are degenerate. The 3s, 3p, and 3d subshells all have n = 3.
3. Ignoring electron spin, what is the total number of degenerate spatial orbitals in the n = 4 shell of a hydrogenic atom?
A.
4
B.
8
C.
16
D.
32
Correct Answer:
16
Explanation:
For a given n, the total number of spatial orbitals is the sum of 2l + 1 over l = 0 to n - 1, which equals n². For n = 4, the degeneracy is 4² = 16.
4. For a hydrogenic atom, which statement correctly compares the energies of the 4s, 4p, 4d, and 4f subshells?
A.
E(4s) < E(4p) < E(4d) < E(4f)
B.
E(4s) > E(4p) > E(4d) > E(4f)
C.
E(4s) = E(4p) = E(4d) = E(4f)
D.
Only 4s and 4p have equal energies
Correct Answer:
E(4s) = E(4p) = E(4d) = E(4f)
Explanation:
For hydrogenic species, the energy of an electron depends only on n and is independent of l. Therefore, all four n = 4 subshells are degenerate.
5. A hydrogenic shell contains 25 degenerate spatial orbitals. Which subshell is not part of this shell?
A.
5s
B.
5p
C.
5d
D.
6s
Correct Answer:
6s
Explanation:
A shell with 25 spatial orbitals has n² = 25, so n = 5. The allowed subshells are 5s, 5p, 5d, 5f, and 5g; 6s belongs to n = 6.
6. In a hydrogenic atom, how many degenerate subshells have exactly 7 spatial orbitals in the n = 7 shell?
A.
0
B.
1
C.
2
D.
7
Correct Answer:
1
Explanation:
A subshell has 2l + 1 spatial orbitals. Exactly 7 orbitals requires l = 3, corresponding only to the 7f subshell. Since all n = 7 subshells are degenerate, the number of such subshells is 1.
7. For a hydrogenic species, the 3d subshell is degenerate in energy with which of the following subshells?
A.
2p
B.
3p
C.
4d
D.
4s
Correct Answer:
3p
Explanation:
The 3d subshell has n = 3. In a hydrogenic species, all subshells with the same n, including 3s, 3p, and 3d, have the same energy.
8. Including electron spin, what is the maximum number of electrons that can occupy the complete set of degenerate subshells in the n = 3 shell of a hydrogenic atom?
A.
9
B.
18
C.
27
D.
36
Correct Answer:
18
Explanation:
The n = 3 shell has n² = 9 spatial orbitals distributed among 3s, 3p, and 3d. Each spatial orbital accommodates two spin states, so the total degeneracy including spin is 2n² = 18.
9. Which pair represents subshells that are degenerate in a hydrogenic atom but generally not degenerate in a many-electron atom?
A.
2s and 2p
B.
2p and 3p
C.
3s and 4s
D.
3p and 4d
Correct Answer:
2s and 2p
Explanation:
In a hydrogenic atom, 2s and 2p have the same n and are degenerate. In many-electron atoms, shielding and penetration make subshell energies depend on both n and l, so these subshells generally split.
10. A hydrogenic shell has subshells with azimuthal quantum numbers l = 0, 1, 2, and 3, all at the same energy. What is the principal quantum number of this shell and its total spatial-orbital degeneracy?
A.
n = 3 and 9 orbitals
B.
n = 4 and 16 orbitals
C.
n = 3 and 16 orbitals
D.
n = 4 and 25 orbitals
Correct Answer:
n = 4 and 16 orbitals
Explanation:
The allowed l values in a shell range from 0 to n - 1. Since the largest value is l = 3, n = 4. The total spatial-orbital degeneracy is n² = 4² = 16.
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