chemistry : class11 Orbital Phase : Shapes of d orbitals : Structure of Atom MCQ Questions and Answers
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Orbital Phase
MCQ questions and answers.
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MCQ Questions
1. For a real d_xy orbital represented by an angular wavefunction proportional to xy, which phase pattern is correct in the four xy-plane quadrants?
A.
Positive in quadrants I and III, negative in quadrants II and IV
B.
Positive in quadrants I and II, negative in quadrants III and IV
C.
Positive in all four quadrants because d orbitals have l = 2
D.
Negative in quadrants I and III, positive in quadrants II and IV
Correct Answer:
Positive in quadrants I and III, negative in quadrants II and IV
Explanation:
Since the angular part is proportional to xy, its sign is positive when x and y have the same sign and negative when they have opposite signs. Thus quadrants I and III have one phase, while II and IV have the opposite phase.
2. Using the conventional phase choice for d_x2-y2, with its wavefunction proportional to x² − y², what are the phases along the positive x-axis and positive y-axis, respectively?
A.
Positive along x and positive along y
B.
Negative along x and positive along y
C.
Positive along x and negative along y
D.
Negative along x and negative along y
Correct Answer:
Positive along x and negative along y
Explanation:
On the positive x-axis, y = 0, so x² − y² is positive. On the positive y-axis, x = 0, so x² − y² is negative. The opposite overall convention would reverse both signs, but the relative phase remains opposite.
3. What happens to the phase of a d-orbital wavefunction when the position vector is inverted, r becomes −r?
A.
The phase always reverses because the orbital has angular nodes
B.
The phase remains unchanged because d orbitals have even parity
C.
The phase becomes zero because inversion places the electron on a nodal surface
D.
The phase changes only for d_xy and d_x2-y2 orbitals
Correct Answer:
The phase remains unchanged because d orbitals have even parity
Explanation:
For an orbital with angular momentum quantum number l, inversion produces a factor (−1)^l. For d orbitals, l = 2, so (−1)^2 = +1. Therefore, opposite points have the same wavefunction phase.
4. In a d_xy orbital, what is the phase change when a path crosses the xz-plane but does not cross the yz-plane?
A.
The phase changes sign once
B.
The phase changes sign twice and returns to its original value
C.
The phase remains unchanged because the xz-plane is not a nodal plane
D.
The wavefunction changes from real to imaginary
Correct Answer:
The phase changes sign once
Explanation:
The d_xy wavefunction is proportional to xy. The xz-plane has y = 0 and is therefore a nodal plane. Crossing it changes the sign of y while x retains its sign, so the product xy changes sign once.
5. For the conventional d_z2 orbital, whose angular factor is proportional to 2z² − x² − y², what is the relative phase between the lobes along the z-axis and the region in the xy-plane?
A.
The z-axis lobes and the xy-plane region have the same phase
B.
The z-axis lobes and the xy-plane region have opposite phases
C.
Both regions have zero phase because d_z2 has no angular dependence
D.
The phase changes only when moving from positive z to negative z
Correct Answer:
The z-axis lobes and the xy-plane region have opposite phases
Explanation:
Along the z-axis, x = y = 0, so the angular factor is positive. In the xy-plane, z = 0, making the factor −x² − y², which is negative. Hence these regions have opposite phases.
6. A d_xy orbital is physically rotated through 90° about the z-axis. Relative to the original d_xy function and the fixed coordinate axes, how is the rotated orbital represented?
A.
As d_xy with the same overall phase
B.
As −d_xy, indicating reversal of the phase pattern relative to the axes
C.
As d_x2-y2 because every 90° rotation converts d_xy into d_x2-y2
D.
As a spherical orbital with no phase variation
Correct Answer:
As −d_xy, indicating reversal of the phase pattern relative to the axes
Explanation:
A 90° rotation maps the angular factor xy into (−y)(x) = −xy when expressed in the original fixed axes. Thus the spatial phase pattern corresponds to −d_xy, although an overall sign itself is a convention.
7. At a point in the xy-plane where x and y are both nonzero and have opposite signs, what is the phase of the conventional d_xy wavefunction proportional to xy?
A.
Positive
B.
Negative
C.
Zero
D.
Indeterminate because the point is not on an axis
Correct Answer:
Negative
Explanation:
When x and y have opposite signs, their product xy is negative. The wavefunction therefore has the phase opposite to that in regions where x and y have the same sign.
8. Two lobes of the same d-orbital approach each other across a nodal plane. Which statement correctly describes the wavefunction phase immediately on the two sides of that plane?
A.
The wavefunction has the same nonzero sign on both sides
B.
The wavefunction is zero at the plane and has opposite signs on the two sides
C.
The wavefunction is zero throughout both lobes
D.
The phase changes continuously without passing through zero
Correct Answer:
The wavefunction is zero at the plane and has opposite signs on the two sides
Explanation:
A nodal plane is a surface where the wavefunction is zero. For the real d-orbitals considered here, crossing such a plane changes the sign of the angular wavefunction, so adjacent lobes have opposite phases.
9. For d_xy, a path crosses both the xz-plane and the yz-plane sequentially, without crossing any other nodal surface. What is the net phase relation between the initial and final regions?
A.
The final phase is opposite to the initial phase
B.
The final phase is the same as the initial phase
C.
The final wavefunction must be zero
D.
The phase becomes undefined because two nodal planes are crossed
Correct Answer:
The final phase is the same as the initial phase
Explanation:
Crossing either nodal plane changes the sign of d_xy once. Crossing both planes produces two sign reversals, so the net factor is (−1)² = +1 and the initial and final phases are the same.
10. Which statement best distinguishes orbital phase from electron density for a real d-orbital?
A.
Opposite orbital phases always correspond to different electron densities
B.
The sign of the wavefunction indicates phase, whereas electron density depends on its square and cannot distinguish opposite phases
C.
Electron density is negative in lobes having negative phase
D.
Orbital phase has no relation to the sign of the wavefunction
Correct Answer:
The sign of the wavefunction indicates phase, whereas electron density depends on its square and cannot distinguish opposite phases
Explanation:
For a real orbital, phase is represented by the sign of the wavefunction. Electron density is proportional to ψ², so regions with ψ and −ψ have identical density even though their phases are opposite.
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