chemistry : class11 Angular Nodes : Shapes of d orbitals : Structure of Atom MCQ Questions and Answers
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Angular Nodes
MCQ questions and answers.
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MCQ Questions
1. How many angular nodes are present in every 3d orbital, irrespective of whether its shape is dxy, dyz, dz2, dx2-y2, or dxz?
A.
0
B.
1
C.
2
D.
3
Correct Answer:
2
Explanation:
For any d orbital, the azimuthal quantum number is l = 2. The number of angular nodes equals l, so every 3d orbital has exactly two angular nodes.
2. Which pair of planes represents the angular nodal surfaces of the dxy orbital?
A.
The xy-plane and the yz-plane
B.
The xz-plane and the yz-plane
C.
The planes x = y and x = -y
D.
The planes z = x and z = -x
Correct Answer:
The xz-plane and the yz-plane
Explanation:
The angular part of dxy is proportional to xy. It becomes zero when x = 0 or y = 0, corresponding to the yz-plane and xz-plane, respectively.
3. The two angular nodal planes of the dx2-y2 orbital are oriented as:
A.
The xz-plane and the yz-plane
B.
The xy-plane and a plane perpendicular to it
C.
The planes x = y and x = -y
D.
Two cones symmetric about the z-axis
Correct Answer:
The planes x = y and x = -y
Explanation:
The angular part of dx2-y2 is proportional to x2 - y2 = (x - y)(x + y). Therefore, its angular nodes are the planes x = y and x = -y.
4. For the dz2 orbital, the angular nodal surfaces are best described as:
A.
The xz-plane and the yz-plane
B.
Two planes containing the z-axis and making 45° with the x-axis
C.
Two cones with their common axis along the z-axis
D.
A single spherical surface centered at the nucleus
Correct Answer:
Two cones with their common axis along the z-axis
Explanation:
The angular factor of dz2 is proportional to 3cos2(theta) - 1. It vanishes at cos(theta) = plus or minus 1 divided by the square root of 3, producing two conical angular nodal surfaces around the z-axis.
5. An orbital has an angular wavefunction proportional to z(x + y). Which angular nodal surfaces does it possess?
A.
The xy-plane and the plane x + y = 0
B.
The xz-plane and the yz-plane
C.
The planes x = y and x = -y
D.
Two cones around the x-axis
Correct Answer:
The xy-plane and the plane x + y = 0
Explanation:
The wavefunction is zero when z = 0 or x + y = 0. These conditions correspond to the xy-plane and the plane x + y = 0, giving the two angular nodes.
6. A real d-orbital wavefunction is formed as a suitable linear combination of dxy and dx2-y2. Which statement about its angular nodes is necessarily true?
A.
It has one angular node because the two component orbitals overlap
B.
It has two angular nodes, generally represented by two planes through the nucleus
C.
It has four angular nodes because both component orbitals have two nodes
D.
It has no angular nodes because linear combination removes nodal surfaces
Correct Answer:
It has two angular nodes, generally represented by two planes through the nucleus
Explanation:
Both dxy and dx2-y2 belong to the l = 2 set, so any nonzero real linear combination remains a d-type angular function with two angular nodes. For combinations involving only x and y coordinates, the nodal directions generally form two planes through the nucleus.
7. Which observation most directly distinguishes the angular nodes of dz2 from those of dxy?
A.
dz2 has two angular nodes, whereas dxy has none
B.
dz2 has conical angular nodes, whereas dxy has planar angular nodes
C.
dz2 has radial nodes, whereas dxy has angular nodes
D.
dz2 has one angular node, whereas dxy has two
Correct Answer:
dz2 has conical angular nodes, whereas dxy has planar angular nodes
Explanation:
Both orbitals have two angular nodes because both are d orbitals. However, dz2 has conical nodal surfaces, while dxy vanishes in the two coordinate planes xz and yz.
8. For the orbital dxy, along which direction does the electron probability density remain zero because of an angular node?
A.
A direction in the xy-plane halfway between the x- and y-axes
B.
The positive x-axis only
C.
The direction making 54.7° with the z-axis
D.
Every direction in the xy-plane
Correct Answer:
The positive x-axis only
Explanation:
The dxy wavefunction is proportional to xy and vanishes when x = 0 or y = 0. The positive x-axis satisfies y = 0, so it lies on the yz-plane nodal surface and has zero probability density.
9. At the polar angle theta satisfying cos(theta) = 1 divided by the square root of 3, what occurs for the dz2 orbital?
A.
The orbital reaches a maximum positive amplitude
B.
The orbital has an angular node
C.
The orbital has a radial node
D.
The orbital becomes identical to dxy
Correct Answer:
The orbital has an angular node
Explanation:
The angular factor of dz2 is proportional to 3cos2(theta) - 1. Substitution of cos(theta) = 1 divided by the square root of 3 makes this factor zero, identifying a conical angular node.
10. If an orbital has exactly two angular nodes and no angular dependence beyond that required for l = 2, which orbital family does it belong to?
A.
s orbitals
B.
p orbitals
C.
d orbitals
D.
f orbitals
Correct Answer:
d orbitals
Explanation:
The number of angular nodes equals the azimuthal quantum number l. Two angular nodes therefore correspond to l = 2, which defines the d-orbital family.
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