chemistry : class11 Orbital Degeneracy : Concept of orbitals : Structure of Atom MCQ Questions and Answers
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Orbital Degeneracy
MCQ questions and answers.
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MCQ Questions
1. For a hydrogen atom in the absence of external electric and magnetic fields, which complete set of orbitals is degenerate with the 3s orbital?
A.
Only the three 3p orbitals
B.
The three 3p and five 3d orbitals
C.
The five 3d and seven 4f orbitals
D.
Only the five 3d orbitals
Correct Answer:
The three 3p and five 3d orbitals
Explanation:
In a hydrogen atom, orbital energy depends only on the principal quantum number n. Thus, all nine orbitals with n = 3—one 3s, three 3p, and five 3d orbitals—are degenerate.
2. How many orbitals belong to the degenerate n = 4 level of a hydrogen atom, excluding spin degeneracy?
A.
4
B.
8
C.
16
D.
32
Correct Answer:
16
Explanation:
For a hydrogen atom, all orbitals having the same principal quantum number are degenerate. The number of orbitals in the nth shell is n², so for n = 4 the degeneracy is 4² = 16.
3. Which pair of orbitals is degenerate in a hydrogen atom but not degenerate in a many-electron atom under ordinary conditions?
A.
2pₓ and 2pᵧ
B.
3dxy and 3dx²−y²
C.
2s and 2pᵧ
D.
4fxyz and 4fx(x²−3y²)
Correct Answer:
2s and 2pᵧ
Explanation:
In hydrogen, 2s and 2p orbitals have the same n value and are therefore degenerate. In many-electron atoms, penetration and shielding make 2s lower in energy than 2p, whereas orbitals within the same subshell remain degenerate in the absence of external fields.
4. A hydrogen-like ion has an electron in the n = 3 shell. How many distinct orbitals are degenerate with its 3pₓ orbital?
A.
3
B.
5
C.
9
D.
18
Correct Answer:
9
Explanation:
For a hydrogen-like ion, energy depends only on n. The n = 3 shell contains one 3s, three 3p, and five 3d orbitals, giving a total of 1 + 3 + 5 = 9 degenerate orbitals.
5. In a hydrogen atom, which statement correctly compares the energies of the 4s, 4p, 4d, and 4f orbitals?
A.
4s < 4p < 4d < 4f
B.
4f < 4d < 4p < 4s
C.
All four have the same energy
D.
Only 4s and 4p have the same energy
Correct Answer:
All four have the same energy
Explanation:
For hydrogen, orbital energy is determined solely by the principal quantum number. Since all four orbitals have n = 4, they are degenerate, regardless of their azimuthal quantum numbers.
6. What is the total number of orbitals degenerate with a 2p orbital in a hydrogen atom, including the 2p orbital itself but excluding electron spin?
A.
3
B.
4
C.
6
D.
8
Correct Answer:
4
Explanation:
The 2p orbital belongs to the n = 2 shell. In hydrogen, the 2s orbital and all three 2p orbitals have the same energy, so the total orbital degeneracy is 1 + 3 = 4.
7. Which change would remove the degeneracy between the 2s and 2p orbitals of a hydrogen atom while directly affecting their orbital energies?
A.
Changing the orientation label from pₓ to pᵧ
B.
Applying an external electric field
C.
Counting the orbitals in the n = 2 shell
D.
Replacing 2pₓ by 2pᵧ without applying a field
Correct Answer:
Applying an external electric field
Explanation:
An external electric field can lift the accidental degeneracy between orbitals having the same n but different l values, such as 2s and 2p. Merely changing the orientation label does not alter degeneracy in the absence of an external field.
8. For a hydrogen-like species, the energy of which pair of orbitals is necessarily equal in the absence of external fields?
A.
2s and 3s
B.
2p and 3p
C.
3s and 3d
D.
3p and 4p
Correct Answer:
3s and 3d
Explanation:
In a hydrogen-like species, all orbitals with the same principal quantum number are degenerate. The 3s and 3d orbitals both have n = 3, whereas the other pairs have different principal quantum numbers.
9. A hydrogen atom has an n = 5 shell. Which expression gives the number of orbitals degenerate with any one orbital in this shell, excluding spin?
A.
2n = 10
B.
n = 5
C.
n² = 25
D.
2n² = 50
Correct Answer:
n² = 25
Explanation:
In hydrogen, every allowed orbital with a given principal quantum number n has the same energy. The total number of such orbitals is the sum of 2l + 1 over l = 0 to n − 1, which equals n²; therefore, for n = 5 it is 25.
10. In a many-electron atom without external fields, which set contains orbitals that remain degenerate because each set member has the same n and l values?
A.
3s, 3pₓ, and 3dxy
B.
3pₓ, 3pᵧ, and 3p_z
C.
2s, 3s, and 4s
D.
3dxy, 4dxy, and 5dxy
Correct Answer:
3pₓ, 3pᵧ, and 3p_z
Explanation:
In a many-electron atom, orbitals within the same subshell have equal energy when no external field is present. The three 3p orbitals share n = 3 and l = 1, so they are degenerate; orbitals with different n or l generally are not.
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