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(D) The angular wave function for $p$-orbitals is given by:$A(	heta, \phi) = \sqrt{\frac{3}{4\pi}} \cos 	heta$ for $p_z$ orbital.Given expression is

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$2p_z$

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(D) The angular wave function for $p$-orbitals is given by:$A(	heta, \phi) = \sqrt{\frac{3}{4\pi}} \cos 	heta$ for $p_z$ orbital.Given expression is $\frac{1}{2}\sqrt{\frac{3}{\pi}}\cos 	heta = \sqrt{\frac{1}{4}} \cdot \sqrt{\frac{3}{\pi}} \cos 	heta = \sqrt{\frac{3}{4\pi}} \cos 	heta$.Since the angular part depends only on $	heta$ and involves $\cos 	heta$,it corresponds to the $p_z$ orbital,which is oriented along the $Z$-axis.For $p_z$ orbital,the nodal plane is the $XY$ plane,where $	heta = 90^{\circ}$ and $\cos 90^{\circ} = 0$.

The angular wave function $A(\theta, \phi)$ for a given atomic orbital is $\frac{1}{2}\sqrt{\frac{3}{\pi}}\cos \theta$ in the polar coordinate system. Identify the orbital.

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