Question

Select the incorrect option regarding following plot.

• A. Minimum possible angular node will be zero.
• B. It is for n -l -1 =0
• C. Wave function does not depend on angle $\theta$ and $\varphi$.
• D. It gives probability of finding the electron at a point at distance r from the nucleus.

Answer 1

The correct option is C Wave function does not depend on angle $\theta$ and $\varphi$.

Schrodinger Equation in polar coordinates is given as

$\frac{-n^2}{8{\pi }^2\mu }[\frac{1}{r^2}\frac{\delta }{\delta r}\left(r^2\frac{\delta }{\delta r}\right)+\frac{1}{r^2\sin \theta }\frac{\delta }{r\theta }\left(\sin \theta \frac{\delta }{\delta \theta }\right)+\frac{1}{r^2{\sin }^2\theta }\frac{{\delta }^2}{\delta {\varphi }^2}]\Psi =E\Psi$

Thus $\Psi$ depends upon $r,\theta$ & $\varphi$

$Ps{i}_{(r,\theta ,\varphi )}=R_{\left(r\right)}{\Theta }_{\left(\theta \right)}{\Phi }_{\left(\varphi \right)}$

Thus the statement that wave function does not depend on angle $\theta$ and $\varphi$ is incorrect.

$R_{\left(r\right)}$=Radial function which depends upon $r$.

${\Theta }_{\left(\theta \right)}$= Function depend on $\theta$ (Angular).

${\Phi }_{\left(\varphi \right)}$= Angular function depend on $\varphi$.