chemistry : class11 Dumbbell-and-Torus Geometry : Shapes of d orbitals : Structure of Atom MCQ Questions and Answers
Practice important
Dumbbell-and-Torus Geometry
MCQ questions and answers.
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MCQ Questions
1. Which d orbital has an angular boundary surface consisting of two elongated lobes aligned along the z-axis and a torus encircling the nucleus in the xy-plane?
A.
dxy
B.
dxz
C.
dyz
D.
dz2
Correct Answer:
dz2
Explanation:
The dz2 orbital is uniquely represented by two lobes along the z-axis with a doughnut-shaped torus around the nucleus in the xy-plane.
2. In the characteristic dumbbell-and-torus model of the dz2 orbital, the torus is oriented primarily in which plane?
A.
The yz-plane
B.
The xz-plane
C.
The xy-plane
D.
A plane equally inclined to all three coordinate planes
Correct Answer:
The xy-plane
Explanation:
The two principal lobes of dz2 point along z, while the torus surrounds the nucleus in the perpendicular xy-plane.
3. Which geometric feature distinguishes dz2 from the other four d-orbital shapes most directly?
A.
Its four lobes lie between coordinate axes
B.
Its four lobes lie directly on coordinate axes
C.
It contains two axial lobes together with a toroidal region
D.
It has a spherical shell surrounding four planar lobes
Correct Answer:
It contains two axial lobes together with a toroidal region
Explanation:
The defining visual feature of dz2 is the combination of two opposite lobes along the z-axis and a torus around the central region.
4. If the dumbbell-and-torus shape of dz2 is viewed along the z-axis toward the nucleus, what broad cross-sectional appearance is expected from the axial lobes?
A.
Two separated lobes appear directly along the viewing direction
B.
The axial lobes project toward the center, while the torus appears as a circular ring around it
C.
Four lobes appear at 90° intervals in the viewing plane
D.
Only a single spherical lobe is visible
Correct Answer:
The axial lobes project toward the center, while the torus appears as a circular ring around it
Explanation:
Looking along z looks into the ends of the two axial lobes, whereas the torus lies around the central axis and is seen as a ring-like feature.
5. Which statement correctly compares the geometric orientation of dz2 with dxy?
A.
Both have a torus in the xy-plane and two axial lobes
B.
dz2 has axial lobes and a torus, whereas dxy has four lobes between the x- and y-axes
C.
dz2 has four lobes between axes, whereas dxy has two lobes and a torus
D.
Both consist of four lobes directed along the coordinate axes
Correct Answer:
dz2 has axial lobes and a torus, whereas dxy has four lobes between the x- and y-axes
Explanation:
The dumbbell-and-torus geometry belongs to dz2; dxy instead has four lobes arranged in the xy-plane between the x and y axes.
6. A three-dimensional orbital model shows a circular torus centered on the nucleus and pierced by an axis passing through two opposite elongated lobes. Which axis must pass through the elongated lobes?
A.
The x-axis
B.
The y-axis
C.
The z-axis
D.
No coordinate axis; the lobes must lie diagonally between axes
Correct Answer:
The z-axis
Explanation:
This is the characteristic orientation of dz2: the lobes extend along z, and the torus occupies the surrounding xy-plane.
7. Which transformation of the standard dz2 drawing preserves its dumbbell-and-torus geometry while changing its apparent orientation in space?
A.
Rotating the entire orbital model so the lobe axis points along a different laboratory axis
B.
Replacing the torus by four planar lobes
C.
Moving the torus entirely into one axial lobe
D.
Flattening both lobes into a single circular disk
Correct Answer:
Rotating the entire orbital model so the lobe axis points along a different laboratory axis
Explanation:
A spatial rotation changes the drawing's orientation but preserves the essential geometry of two opposite lobes and a perpendicular torus.
8. In the dumbbell-and-torus representation of dz2, how is the torus positioned relative to the two elongated lobes?
A.
It lies inside one lobe and is parallel to the lobe axis
B.
It intersects the lobes at their far ends and is perpendicular to the nucleus
C.
It surrounds the central region and is oriented perpendicular to the lobe axis
D.
It replaces the region between the two lobes with four separate disks
Correct Answer:
It surrounds the central region and is oriented perpendicular to the lobe axis
Explanation:
For dz2, the torus is centered around the nucleus in the xy-plane, perpendicular to the z-directed lobe axis.
9. A student identifies an orbital as dz2 because it has two lobes, but the drawing lacks any toroidal central region. What is the best correction?
A.
The drawing is complete because every d orbital has exactly two lobes
B.
The drawing is incomplete because dz2 includes a torus in addition to the two lobes
C.
The drawing must represent dxy because dxy always has two lobes
D.
The drawing cannot represent any orbital because toroidal regions are impossible
Correct Answer:
The drawing is incomplete because dz2 includes a torus in addition to the two lobes
Explanation:
The torus is an essential part of the characteristic dz2 shape; showing only the two axial lobes omits its central geometry.
10. Which description would unambiguously identify the dumbbell-and-torus geometry rather than a four-lobed cloverleaf geometry?
A.
Four equivalent lobes arranged in one plane between two coordinate axes
B.
Four equivalent lobes directed along the positive and negative coordinate directions
C.
Two opposite lobes on one axis with a ring-like region around the central axis
D.
Four lobes arranged tetrahedrally around the nucleus
Correct Answer:
Two opposite lobes on one axis with a ring-like region around the central axis
Explanation:
The combination of two opposite axial lobes and a ring-like torus uniquely characterizes the dz2 orbital geometry.