chemistry : class11 Orbital Symmetry : Shapes of d orbitals : Structure of Atom MCQ Questions and Answers
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Orbital Symmetry
MCQ questions and answers.
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MCQ Questions
1. Which statement most accurately distinguishes the symmetry of the d_xy orbital from that of the d_x2-y2 orbital?
A.
Both have lobes along the x- and y-axes, but d_xy has four lobes while d_x2-y2 has two
B.
d_xy has lobes between the x- and y-axes, whereas d_x2-y2 has lobes directed along these axes
C.
d_xy is spherically symmetric, whereas d_x2-y2 is cylindrically symmetric
D.
d_xy has lobes along the z-axis, whereas d_x2-y2 has lobes in the xy-plane
Correct Answer:
d_xy has lobes between the x- and y-axes, whereas d_x2-y2 has lobes directed along these axes
Explanation:
The d_xy orbital has four lobes lying between the x- and y-axes in the xy-plane. The d_x2-y2 orbital also lies in the xy-plane, but its four lobes point directly along the positive and negative x- and y-axes.
2. How many angular nodal planes pass through the nuclei for a d orbital, and which orbital illustrates two such planes coinciding with the xz and yz planes?
A.
One; d_z2
B.
Two; d_xy
C.
Two; d_x2-y2
D.
Three; d_xz
Correct Answer:
Two; d_xy
Explanation:
Every d orbital has angular quantum number l = 2 and therefore has two angular nodes. For d_xy, the xz and yz planes are nodal planes because the orbital wavefunction becomes zero whenever x = 0 or y = 0.
3. A 90° rotation about the z-axis changes the sign of the wavefunction of which orbital while preserving its overall shape?
A.
d_z2
B.
d_x2-y2
C.
d_xz
D.
d_yz
Correct Answer:
d_x2-y2
Explanation:
Under a 90° rotation about the z-axis, the x2 - y2 angular factor changes to y2 - x2, which is the negative of the original function. Thus the shape is unchanged, but the phase of every lobe is reversed.
4. Which transformation interchanges d_xz and d_yz without introducing a change in their radial part?
A.
Interchanging the x- and y-axes
B.
Reflecting through the xy-plane
C.
Inverting all three axes simultaneously
D.
Rotating only about the z-axis by 180°
Correct Answer:
Interchanging the x- and y-axes
Explanation:
The angular factors are proportional to xz for d_xz and yz for d_yz. Interchanging x and y converts xz into yz, thereby interchanging the two orbitals while leaving the radial dependence unchanged.
5. Which d orbital remains unchanged in sign under every rotation about the z-axis, although its electron-density pattern is not spherical?
A.
d_xy
B.
d_xz
C.
d_x2-y2
D.
d_z2
Correct Answer:
d_z2
Explanation:
The d_z2 orbital depends on the angular factor 2z2 - x2 - y2, which is independent of the azimuthal angle around the z-axis. Therefore, it has cylindrical symmetry about z and does not change sign under rotations about that axis.
6. Which pair of d orbitals has nodal planes that include the z-axis and differs only in the azimuthal orientation of its lobes?
A.
d_z2 and d_x2-y2
B.
d_xz and d_yz
C.
d_xy and d_z2
D.
d_x2-y2 and d_z2
Correct Answer:
d_xz and d_yz
Explanation:
Both d_xz and d_yz have two lobes in planes containing the z-axis. Their nodal planes are respectively the yz and xz planes, so they have the same type of symmetry but are rotated by 90° around the z-axis.
7. Which statement about the phase symmetry of d orbitals is correct?
A.
All four lobes of every d orbital necessarily have the same phase
B.
Adjacent lobes of d_xy and d_x2-y2 have opposite phases
C.
The two lobes of d_z2 always have opposite phases to each other
D.
Phase has no relation to the nodal planes of an orbital
Correct Answer:
Adjacent lobes of d_xy and d_x2-y2 have opposite phases
Explanation:
For d_xy, the sign of the angular factor changes when crossing either the xz or yz nodal plane, so adjacent lobes have opposite phases. The same alternating phase pattern occurs for d_x2-y2 across its nodal planes.
8. A plane contains the z-axis and bisects the angle between the positive x- and y-axes. Which orbital has this plane as a nodal plane?
A.
d_z2
B.
d_xz
C.
d_xy
D.
d_x2-y2
Correct Answer:
d_x2-y2
Explanation:
The plane y = x contains the z-axis and lies midway between the positive x- and y-axes. For d_x2-y2, the angular factor x2 - y2 becomes zero when x = y, making this plane a nodal plane.
9. Which description correctly compares the nodal planes of d_xy and d_x2-y2?
A.
Both have the xy-plane as their only nodal plane
B.
d_xy has xz and yz as nodal planes, while d_x2-y2 has planes bisecting the x- and y-axes
C.
d_xy has planes bisecting the axes as nodal planes, while d_x2-y2 has xz and yz as nodal planes
D.
Both have the xz and yz planes as nodal planes
Correct Answer:
d_xy has xz and yz as nodal planes, while d_x2-y2 has planes bisecting the x- and y-axes
Explanation:
The d_xy function is proportional to xy and vanishes when x = 0 or y = 0, corresponding to the yz and xz planes. The d_x2-y2 function is proportional to x2 - y2 and vanishes when x = y or x = -y, corresponding to planes that bisect the coordinate axes.
10. Which linear combination of d_x2-y2 and d_xy produces an orbital whose four lobes are rotated by 22.5° relative to those of d_x2-y2 in the xy-plane?
A.
d_x2-y2 + d_xy
B.
d_x2-y2 - d_xy
C.
d_x2-y2 + 2d_xy
D.
2d_x2-y2 + d_xy
Correct Answer:
d_x2-y2 + d_xy
Explanation:
The angular dependence of d_x2-y2 + d_xy is proportional to cos 2φ + sin 2φ, which equals a constant times cos(2φ - 45°). Therefore, the orbital is rotated by 22.5° because the doubled azimuthal angle shifts by 45°.
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