Which of the following is the correct plot for the probability density $$\psi^2(r)$$ as a function of distance 'r' of the electron form the nucleus for 2s orbital?

1. Identify the Number of Radial Nodes

The number of radial nodes (points where the probability of finding an electron drops to zero) is calculated using the formula:

$$\text{Radial Nodes} = n - l - 1$$

For a 2s orbital:

• Principal quantum number ($$n$$) = $$2$$
• Azimuthal quantum number ($$l$$) = $$0$$ (for an s-orbital)

$$\text{Radial Nodes} = 2 - 0 - 1 = 1$$

This means the graph must touch the $$x$$-axis (where $$\psi^2 = 0$$) exactly once before eventually tapering off to zero at infinity.

2. Behavior at the Nucleus ($$r = 0$$)

For all s-orbitals, the electron wave function ($$\psi$$) has a finite, non-zero value at the nucleus because there is no angular node passing through the center. Therefore, the probability density $$\psi^2(r)$$ starts at a maximum value on the $$y$$-axis when $$r = 0$$.

Hence, Option B is correct because it matches all the points