Question

The number of given orbitals which have electron density along the axis is _____ $p _x, p _y, p _z, d _{x y}, d _{y z}, d _{x z}, d _z 2, d _x{ }^2-y^2$

Answer 1

Correct Answer: 5

To solve the problem of determining the number of orbitals with electron density along the axis from the given set, we need to analyze each orbital type: $p_x$, $p_y$, $p_z$, $d_{xy}$, $d_{yz}$, $d_{xz}$, $d_{z^2}$, and $d_{x^2-y^2}$.
 

• $p$-orbitals ($p_x$, $p_y$, $p_z$): These are directional and have electron density along their respective axes (i.e., $p_x$ along x-axis, $p_y$ along y-axis, and $p_z$ along z-axis). Thus, each contributes 1 orbital with axis-aligned electron density.
• $d$-orbitals:
  • $d_{xy}$, $d_{yz}$, $d_{xz}$: These orbitals lie between axes and do not have their electron density aligned along any single axis.
  • $d_{z^2}$: This orbital has a distinct shape with electron density along the z-axis.
  • $d_{x^2-y^2}$: Electron density lies along the x and y axes.

Considering the above analysis, the orbitals with electron density along the axis are $p_x$, $p_y$, $p_z$, $d_{z^2}$, and $d_{x^2-y^2}$. Hence, the total count is 5.