Question

Consider a hypothetical atom where ${{p}_{x}},{{p}_{y}},{{p}_{z}},{{d}_{xy}},{{d}_{xz}},{{d}_{yz}}\text{ and }{{\text{d}}_{{{x}^{2}}-{{y}^{2}}}}$ orbital are present for principal quantum number, n = 3. Find the number of other orbitals whose lobes are fully present in the nodal plane of ${{p}_{x}}$ orbital:
[A] 2
[B] 3
[C] 4
[D] 5

Answer 1

HINT: To solve this, firstly find out the axis on which the nodal plane of ${{p}_{x}}$ orbital lies on. Then, find out the plane or axis in which the lobes of the other orbitals lie. See lobes of which orbitals lie in the plane through which the nodal plane of ${{p}_{x}}$ passes in order to find out the required solution.

COMPLETE STEP BY STEP SOLUTION: To answer this, firstly let us discuss what a nodal plane is. An angular node is also known as a nodal plane. We can define the nodal plane as the region around an atomic nucleus where there exists zero probability of finding an electron. A nodal plane is basically a plane that passes through the nucleus.
Now, let us discuss the nodal planes of the orbitals mentioned. For ${{p}_{x}}$, the nodal plane lies in the Y-Z axis. We have only one nodal plane for p-orbitals. Its lobes lie on the X-axis. Similarly, for ${{p}_{y}}\text{ and }{{p}_{z}}$, the nodal plane lies in the Z-X axis and the X-Y axis and their lobes lie in Y-axis and Z-axis respectively. For d-orbitals, we get 2 nodal planes due to its double dumb bell shape. For ${{d}_{xy}}$ the planes perpendicular to it are Y-Z and Z-X. And these are the nodal planes respectively. Its loves lie in the XY plane. For ${{d}_{yz}}$ the planes perpendicular to it are X-Y and Z-X and these are the nodal planes respectively. Its lobes lie in the YZ plane. For ${{d}_{zx}}$ the planes perpendicular to it are X-Y and Y-Z and these are the nodal planes respectively. Its lobes lie in the ZX plane. And lastly, for ${{d}_{{{x}^{2}}-{{y}^{2}}}}$ the nodal plane lies in X+Y = 0 and X-Y = 0. The lobes lie in the YZ plane. We can see from the above discussion that nodal plane of ${{p}_{x}}$ is in YZ axis and the lobes of ${{d}_{yz}}$ and ${{d}_{{{x}^{2}}-{{y}^{2}}}}$ lie completely in the YZ axis.

Therefore, the correct answer is option [A] 2

NOTE: In a molecular orbital there are two types of nodes – angular node and radial node. We have already discussed angular nodes in the above discussion.
A radial node is the spherical surface where the probability of finding an electron is zero.
The number of radial nodes increases with increase in principal quantum number However, the number of nodal planes depends upon the shape of the orbital. We know the shape of s-orbital is sphere i.e. there is just a sphere of electron density. Shape of the p-orbital is dumbbell shaped and that of d-orbital is clover shaped, as if two dumbbell shapes are placed beside each other. For s-orbitals, there are zero nodal planes; for p-orbitals we have one nodal plane and for d-orbitals, the number of nodal planes is 2.