chemistry : class11 Electron Density Distribution : Shapes of d orbitals : Structure of Atom MCQ Questions and Answers
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Electron Density Distribution
MCQ questions and answers.
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MCQ Questions
1. For a dxy orbital, along which directions is the electron density exactly zero because of angular nodal planes?
A.
Along the x-axis and y-axis
B.
Along the lines x = y and x = -y
C.
Along the z-axis only
D.
Along all three Cartesian axes
Correct Answer:
Along the x-axis and y-axis
Explanation:
The angular part of a dxy orbital is proportional to xy. Hence its wavefunction, and therefore its electron density, is zero whenever x = 0 or y = 0. These conditions define the yz-plane and xz-plane, so the x- and y-axes lie in nodal planes.
2. Which statement correctly compares the electron-density orientation of the dx2-y2 and dxy orbitals?
A.
Both have maximum density along the z-axis
B.
dx2-y2 has density maxima along the x- and y-axes, whereas dxy has density maxima between these axes in the xy-plane
C.
dx2-y2 has density maxima between the x- and y-axes, whereas dxy has density maxima along the x- and y-axes
D.
Both have identical electron-density distributions because they belong to the same d subshell
Correct Answer:
dx2-y2 has density maxima along the x- and y-axes, whereas dxy has density maxima between these axes in the xy-plane
Explanation:
The angular factors are x2 - y2 for dx2-y2 and xy for dxy. The former is largest along the x and y directions, while the latter is zero on those axes and becomes largest along directions between them.
3. At a point in the xy-plane making an angle of 45 degrees with the x-axis, which orbital has zero electron density due to its angular dependence?
A.
dxy
B.
dx2-y2
C.
dz2
D.
All three orbitals have zero density there
Correct Answer:
dx2-y2
Explanation:
In the xy-plane, the angular factor for dx2-y2 is proportional to cos 2phi. At phi = 45 degrees, cos 90 degrees is zero, producing an angular node. The dxy orbital has maximum rather than zero angular density in these diagonal directions.
4. Which description best represents the electron-density distribution of the dz2 orbital?
A.
Four lobes of density confined to the xy-plane along the x- and y-axes
B.
Four lobes of density confined to the xy-plane between the x- and y-axes
C.
Two lobes of density along the z-axis together with a toroidal region of density around the nucleus in the xy-plane
D.
A spherical region of uniform electron density around the nucleus
Correct Answer:
Two lobes of density along the z-axis together with a toroidal region of density around the nucleus in the xy-plane
Explanation:
The dz2 angular function is proportional to 3cos2 theta - 1. Its electron density is concentrated in two z-directed lobes and also forms a torus around the nucleus in the equatorial plane.
5. Why can a d orbital have zero electron density along a particular direction even though an electron occupies that orbital?
A.
The electron disappears from that direction because of spin pairing
B.
The wavefunction changes sign across an angular nodal surface and becomes zero on that surface
C.
The radial distance is necessarily infinite in that direction
D.
The orbital contains no angular component
Correct Answer:
The wavefunction changes sign across an angular nodal surface and becomes zero on that surface
Explanation:
Electron density is proportional to the square of the wavefunction. At an angular node, the wavefunction itself is zero, so the probability density is zero there, even though the orbital has nonzero density in neighboring regions.
6. A dxy orbital is examined at two points having the same distance from the nucleus: one lies along the x-axis and the other lies in a direction halfway between the x- and y-axes in the xy-plane. Which comparison is correct?
A.
The density is zero at both points
B.
The density is greater along the x-axis
C.
The density is zero along the x-axis and maximal in the halfway direction, apart from radial factors
D.
The density is independent of direction because both points have the same radial distance
Correct Answer:
The density is zero along the x-axis and maximal in the halfway direction, apart from radial factors
Explanation:
For dxy, the angular factor is proportional to sin 2phi. It vanishes at phi = 0 degrees on the x-axis and reaches its largest magnitude at phi = 45 degrees, so the density is greatest in the diagonal directions of the xy-plane.
7. How many angular nodal planes are associated with every d orbital, and what do they imply about electron density?
A.
Zero; the density is spherical
B.
One; the density is divided into two regions
C.
Two; the density is zero on two angular nodal surfaces
D.
Three; the density is zero along all Cartesian axes
Correct Answer:
Two; the density is zero on two angular nodal surfaces
Explanation:
A d orbital has angular quantum number l = 2, so it possesses two angular nodes. On these nodal surfaces the wavefunction and electron density are zero, producing the characteristic directional distribution of d orbitals.
8. For the dx2-y2 orbital, which set of directions corresponds to angular nodes in the xy-plane?
A.
The positive and negative x-axis
B.
The positive and negative y-axis
C.
The lines x = y and x = -y
D.
The positive and negative z-axis
Correct Answer:
The lines x = y and x = -y
Explanation:
The angular factor for dx2-y2 is proportional to x2 - y2. It becomes zero when x2 = y2, corresponding to the diagonal lines x = y and x = -y in the xy-plane. These are directions of zero electron density.
9. Which statement about the sign and magnitude of a d-orbital wavefunction is correct in relation to electron density?
A.
Regions with opposite signs always have different electron densities
B.
The sign itself is not observable as density; regions with equal magnitudes of the wavefunction have equal densities
C.
A negative wavefunction produces negative electron density
D.
Changing the overall sign of the orbital changes its electron-density distribution
Correct Answer:
The sign itself is not observable as density; regions with equal magnitudes of the wavefunction have equal densities
Explanation:
Electron density is given by the squared magnitude of the wavefunction, |psi|2. Therefore positive and negative lobes can have identical densities, and multiplying the entire orbital by -1 does not alter its electron-density distribution.
10. In the xy-plane, the electron density of which orbital varies with the azimuthal angle as the square of cos 2phi, producing maxima on the x- and y-axes and nodes along the diagonal directions?
A.
dxy
B.
dx2-y2
C.
dz2
D.
dyz
Correct Answer:
dx2-y2
Explanation:
For dx2-y2, the angular wavefunction in the xy-plane is proportional to cos 2phi, so its density varies as cos2 2phi. This gives maxima at phi = 0 and 90 degrees and zeros at phi = 45 and 135 degrees.
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