chemistry : class11 Cartesian Axis Alignment : Shapes of d orbitals : Structure of Atom MCQ Questions and Answers
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Cartesian Axis Alignment
MCQ questions and answers.
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MCQ Questions
1. Which statement correctly distinguishes the Cartesian-axis alignment of the dxy and dx²−y² orbitals?
A.
The dxy lobes point along the x- and y-axes, whereas the dx²−y² lobes lie between them.
B.
The dxy lobes lie between the x- and y-axes, whereas the dx²−y² lobes point along the x- and y-axes.
C.
Both orbitals have lobes directed along the z-axis, but differ in the size of their nodal planes.
D.
The dxy orbital lies in the xz-plane, whereas the dx²−y² orbital lies in the yz-plane.
Correct Answer:
The dxy lobes lie between the x- and y-axes, whereas the dx²−y² lobes point along the x- and y-axes.
Explanation:
The dxy orbital has four lobes between the x- and y-axes in the xy-plane. The dx²−y² orbital also lies in the xy-plane, but its four lobes point directly along the x- and y-axes.
2. An orbital has four lobes lying in the xy-plane, with each lobe directed halfway between the positive and negative x- and y-axes. Which orbital is it?
A.
dx²−y²
B.
dxz
C.
dxy
D.
dz²
Correct Answer:
dxy
Explanation:
The dxy orbital is confined to the xy-plane and its lobes are oriented between the Cartesian x- and y-axes, at 45° to each axis.
3. Which d orbital has lobes directed along the positive and negative z-axis and a toroidal region around the z-axis in the xy-plane?
A.
dxy
B.
dxz
C.
dyz
D.
dz²
Correct Answer:
dz²
Explanation:
The dz² orbital is aligned with the z-axis. It consists of two lobes along +z and −z together with a doughnut-shaped region centered around the z-axis in the xy-plane.
4. A d orbital has four lobes in the xz-plane, with lobes lying between the x- and z-axes rather than directly on either axis. Which orbital matches this description?
A.
dxy
B.
dxz
C.
dyz
D.
dx²−y²
Correct Answer:
dxz
Explanation:
The dxz orbital lies in the xz-plane. Its four lobes are positioned between the x- and z-axes within that plane.
5. Which pair of orbitals has the same four-lobed orientation relative to its plane but differs in the Cartesian plane in which it lies?
A.
dxy and dxz
B.
dx²−y² and dz²
C.
dxy and dz²
D.
dx²−y² and dyz
Correct Answer:
dxy and dxz
Explanation:
Both dxy and dxz have four lobes lying between the two named axes of their respective planes. dxy lies in the xy-plane, while dxz lies in the xz-plane.
6. If the x-axis is relabeled as the y-axis and the y-axis as the x-axis, which orbital retains the same Cartesian-axis alignment, apart from a possible sign change in its wavefunction?
A.
dxy
B.
dx²−y²
C.
dxz
D.
dyz
Correct Answer:
dxy
Explanation:
The dxy orbital depends symmetrically on the product xy, so interchanging x and y leaves its geometric orientation unchanged. The dx²−y² orientation changes sign under this interchange, although its probability shape is rotated equivalently.
7. Which orbital is aligned in the yz-plane with its lobes directed between the y- and z-axes?
A.
dxy
B.
dxz
C.
dyz
D.
dx²−y²
Correct Answer:
dyz
Explanation:
The dyz orbital is the four-lobed d orbital located in the yz-plane, with each lobe lying between the y- and z-axes.
8. A 45° rotation about the z-axis changes the Cartesian orientation of the dxy orbital into the orientation characteristic of which orbital?
A.
dz²
B.
dx²−y²
C.
dxz
D.
dyz
Correct Answer:
dx²−y²
Explanation:
Both dxy and dx²−y² lie in the xy-plane. Their four-lobed patterns are rotated by 45° relative to one another: dxy lies between the axes, while dx²−y² lies along the axes.
9. Which set correctly identifies the Cartesian planes containing the four-lobed orbitals dxy, dxz, and dyz, respectively?
A.
xy-plane, xz-plane, yz-plane
B.
xz-plane, yz-plane, xy-plane
C.
yz-plane, xy-plane, xz-plane
D.
xy-plane, yz-plane, xz-plane
Correct Answer:
xy-plane, xz-plane, yz-plane
Explanation:
The subscripts identify the Cartesian plane containing each orbital: dxy lies in the xy-plane, dxz in the xz-plane, and dyz in the yz-plane.
10. Which comparison of dx²−y² and dz² correctly describes their alignment with the Cartesian axes?
A.
Both have four lobes directed between the x-, y-, and z-axes.
B.
dx²−y² has four lobes along the x- and y-axes, whereas dz² has two lobes along the z-axis and a torus in the xy-plane.
C.
dx²−y² has lobes along the z-axis, whereas dz² has four lobes along the x- and y-axes.
D.
Both orbitals are confined to the xy-plane, but dx²−y² has a torus and dz² has four planar lobes.
Correct Answer:
dx²−y² has four lobes along the x- and y-axes, whereas dz² has two lobes along the z-axis and a torus in the xy-plane.
Explanation:
The dx²−y² orbital is oriented directly along the x- and y-axes. The dz² orbital is aligned along the z-axis and includes a toroidal region in the xy-plane.