chemistry : class11 dzx Orbital Shape : Shapes of d orbitals : Structure of Atom MCQ Questions and Answers
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dzx Orbital Shape
MCQ questions and answers.
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MCQ Questions
1. Which pair of mutually perpendicular planes forms the angular nodal planes of the d_zx orbital?
A.
The xy-plane and the yz-plane
B.
The xy-plane and the xz-plane
C.
The yz-plane and the xz-plane
D.
The planes x = z and x = −z
Correct Answer:
The xy-plane and the yz-plane
Explanation:
The angular part of the d_zx orbital is proportional to xz/r². It becomes zero when z = 0, giving the xy-plane, or when x = 0, giving the yz-plane.
2. In which direction is the electron probability density of a d_zx orbital expected to be greatest in the xz-plane?
A.
Along the positive x-axis and positive z-axis
B.
Along the negative x-axis and negative z-axis
C.
Along directions halfway between the x- and z-axes, such as x = z with y = 0
D.
Along the positive and negative y-axes
Correct Answer:
Along directions halfway between the x- and z-axes, such as x = z with y = 0
Explanation:
The d_zx orbital has angular dependence proportional to xz. It vanishes on both the x- and z-axes and is largest in the xz-plane when the magnitudes of x and z are comparable, producing lobes between the axes.
3. A point lies in the xz-plane with x > 0 and z < 0. What is the phase sign of the d_zx wavefunction at that point, relative to a region where x > 0 and z > 0?
A.
It has the same phase because both points lie in the xz-plane
B.
It has the opposite phase because the product xz changes sign
C.
It has zero amplitude because every point in the xz-plane is a nodal point
D.
Its phase cannot be related because d orbitals have no sign
Correct Answer:
It has the opposite phase because the product xz changes sign
Explanation:
For d_zx, the wavefunction changes sign according to xz. When x and z have opposite signs, xz is negative; when they have the same positive sign, xz is positive. The two regions therefore have opposite phases.
4. Which description most accurately represents the spatial shape of a d_zx orbital?
A.
Two lobes centered directly on the z-axis
B.
Four lobes lying between the x- and z-axes in the xz-plane
C.
Four lobes lying between the x- and y-axes in the xy-plane
D.
A spherical cloud with no angular nodes
Correct Answer:
Four lobes lying between the x- and z-axes in the xz-plane
Explanation:
The d_zx orbital has angular factor xz, so its lobes occur where both x and z are nonzero. The orbital is oriented between the x- and z-axes, with four lobes arranged in the xz-plane.
5. For the d_zx orbital, what happens to the wavefunction at every point on the positive z-axis?
A.
It reaches a maximum positive value
B.
It reaches a maximum negative value
C.
It is zero because x = 0 on the z-axis
D.
It is nonzero only because z is positive
Correct Answer:
It is zero because x = 0 on the z-axis
Explanation:
The d_zx angular factor is proportional to xz. On the z-axis, x = 0, so the wavefunction is zero. Thus, the z-axis lies within the yz nodal plane and does not pass through a lobe maximum.
6. Which statement correctly distinguishes the xz-plane from the nodal planes of a d_zx orbital?
A.
The xz-plane is a nodal plane because z is one of the orbital labels
B.
The xz-plane is a nodal plane because it contains two coordinate axes
C.
The xz-plane contains the lobes and is not a nodal plane
D.
The xz-plane is a nodal plane only in the positive quadrant
Correct Answer:
The xz-plane contains the lobes and is not a nodal plane
Explanation:
In the xz-plane, y = 0, but the factor xz can still be nonzero. Therefore, this plane contains the four lobes. The nodal planes are instead xy, where z = 0, and yz, where x = 0.
7. At which set of Cartesian coordinates must the d_zx wavefunction be zero because of its angular shape?
A.
(1, 0, 1)
B.
(1, 1, 1)
C.
(0, 1, 1)
D.
(1, 0, −1)
Correct Answer:
(0, 1, 1)
Explanation:
The d_zx wavefunction is proportional to xz. At (0, 1, 1), x = 0, so the point lies in the yz nodal plane and the wavefunction is zero. The other listed points have both x and z nonzero.
8. Which change in coordinates reverses the phase of a d_zx orbital while leaving its probability density unchanged?
A.
Changing x to −x while keeping z unchanged
B.
Changing x to −x and z to −z simultaneously
C.
Changing y to −y while keeping x and z unchanged
D.
Changing the radial distance while remaining in the same angular direction
Correct Answer:
Changing x to −x while keeping z unchanged
Explanation:
Because the angular factor is xz, changing only x to −x changes xz to −xz, reversing the wavefunction phase. The probability density, proportional to the square of the wavefunction, remains unchanged.
9. How many angular nodal planes does a d_zx orbital possess, and how are they oriented?
A.
One plane, the xz-plane
B.
Two planes, the xy-plane and the yz-plane
C.
Two planes, the planes x = z and x = −z
D.
Three planes, all three coordinate planes
Correct Answer:
Two planes, the xy-plane and the yz-plane
Explanation:
The d_zx orbital has angular dependence proportional to xz. Its zeros occur when x = 0 or z = 0, corresponding to the yz-plane and xy-plane, respectively. The xz-plane is not nodal.
10. A direction in space is specified by x = z ≠ 0 and y = 0. Which description of this direction for the d_zx orbital is correct?
A.
It lies on a nodal plane and has zero amplitude
B.
It passes through the center of one of the four lobes
C.
It lies along a coordinate axis and has zero amplitude
D.
It lies in the yz nodal plane because z is nonzero
Correct Answer:
It passes through the center of one of the four lobes
Explanation:
The condition y = 0 places the direction in the xz-plane, while x = z ≠ 0 places it halfway between the x- and z-axes. These are directions of maximum angular character for the d_zx orbital, corresponding to lobe centers rather than nodes.