Question

The number of following orbital(s) for whic yz plane is a nodal plane is ______

$p_x, p_y, p_z, d_{yz}, d_{x^2-y^2}, s$

Answer 1

1

Answer 2

To determine which of the given orbitals have the yz-plane as a nodal plane, we need to understand the shape and orientation of each orbital and where its wavefunction becomes zero. A nodal plane is a plane where the probability of finding an electron is zero, meaning the angular part of the wavefunction is zero in that plane. The yz-plane is defined by $x=0$.

Let's analyze each orbital:

1. $p_x$ orbital:

   • The $p_x$ orbital has its lobes oriented along the x-axis.
   • The angular part of its wavefunction is proportional to $x$.
   • For a nodal plane, the wavefunction must be zero. So, $x=0$.
   • The plane where $x=0$ is the yz-plane.
   • Therefore, the yz-plane is a nodal plane for the $p_x$ orbital.

2. $p_y$ orbital:

   • The $p_y$ orbital has its lobes oriented along the y-axis.
   • The angular part of its wavefunction is proportional to $y$.
   • Its nodal plane is where $y=0$, which is the xz-plane.
   • Therefore, the yz-plane is not a nodal plane for the $p_y$ orbital.

3. $p_z$ orbital:

   • The $p_z$ orbital has its lobes oriented along the z-axis.
   • The angular part of its wavefunction is proportional to $z$.
   • Its nodal plane is where $z=0$, which is the xy-plane.
   • Therefore, the yz-plane is not a nodal plane for the $p_z$ orbital.

4. $d_{yz}$ orbital:

   • The $d_{yz}$ orbital has its four lobes lying in the yz-plane, between the y and z axes.
   • The angular part of its wavefunction is proportional to $yz$.
   • For a nodal plane, $yz=0$. This implies either $y=0$ (xz-plane) or $z=0$ (xy-plane).
   • Therefore, the yz-plane is not a nodal plane for the $d_{yz}$ orbital.

5. $d_{x^2-y^2}$ orbital:

   • The $d_{x^2-y^2}$ orbital has its four lobes lying along the x and y axes.
   • The angular part of its wavefunction is proportional to $x^2-y^2$.
   • For a nodal plane, $x^2-y^2=0$, which means $x^2=y^2$, or $y = \pm x$. These are two planes containing the z-axis (e.g., the plane containing the z-axis and the line $y=x$, and the plane containing the z-axis and the line $y=-x$).
   • Therefore, the yz-plane is not a nodal plane for the $d_{x^2-y^2}$ orbital.

6. $s$ orbital:

   • An $s$ orbital is spherically symmetric.
   • It has no angular nodes (nodal planes), only radial nodes (spherical nodes).
   • Therefore, the yz-plane is not a nodal plane for an $s$ orbital.

Based on the analysis, only the $p_x$ orbital has the yz-plane as a nodal plane.

The number of orbitals for which the yz-plane is a nodal plane is 1.