The wave function (Psi) of 2s is given byPsi_ | vedclass

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(D) radial node is a point where the probability density and the wave function $(\Psi)$ become zero.For the $2s$ orbital,the wave function is given by

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$r_0 = 2a_0$

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(D) radial node is a point where the probability density and the wave function $(\Psi)$ become zero.For the $2s$ orbital,the wave function is given by:$\Psi_{2s} = \frac{1}{2\sqrt{2\pi}} \left(\frac{1}{a_0}\right)^{3/2} \left(2 - \frac{r}{a_0}\right) e^{-r/2a_0}$At the radial node,$\Psi_{2s} = 0$.Since the exponential term $e^{-r/2a_0}$ cannot be zero,the term in the parenthesis must be zero:$2 - \frac{r_0}{a_0} = 0$Solving for $r_0$:$r_0 = 2a_0$

The wave function $(\Psi)$ of $2s$ is given by
$\Psi_{2s} = \frac{1}{2\sqrt{2\pi}} \left(\frac{1}{a_0}\right)^{3/2} \left(2 - \frac{r}{a_0}\right) e^{-r/2a_0}$
At $r = r_0$,a radial node is formed. Thus,$r_0$ in terms of $a_0$ is:

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The wave function $(\Psi)$ of $2s$ is given by$\Psi_{2s} = \frac{1}{2\sqrt{2\pi}} \left(\frac{1}{a_0}\right)^{3/2} \left(2 - \frac{r}{a_0}\right) e^{-r/2a_0}$At $r = r_0$,a radial node is formed. Thus,$r_0$ in terms of $a_0$ is: