Explain the graph of $\psi(r)$ and $\psi^2(r)$ with distance $r$ from the nucleus.

(N/A) $\psi(r)$ vs $r$ graph:
- This graph represents the variation of the wave function with distance from the nucleus. The curve is specific to each orbital.
- The points where the curve crosses the $r$-axis (where $\psi(r) = 0$) represent the radial nodes.
- For the $1s$ orbital,$\psi(r)$ is maximum at $r = 0$ and decreases exponentially. For $2s$,it passes through zero at a certain distance,indicating a node.
$\psi^2(r)$ vs $r$ graph:
- This graph represents the probability density of finding an electron at a distance $r$ from the nucleus.
- Since $\psi^2(r)$ is always positive,the curve remains above the $r$-axis.
- The value of $\psi^2(r)$ decreases as $r$ increases. The points where $\psi^2(r) = 0$ correspond to radial nodes,where the probability of finding an electron is zero.