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

Solution

We have the wave function for the $$2s$$ orbital:

$$\Psi_{2s} = \frac{1}{2\sqrt{2\pi}}\left(\frac{1}{a_0}\right)^{1/2}\left(2 - \frac{r}{a_0}\right)e^{-r/2a_0}$$

A radial node occurs where $$\Psi = 0$$. Since the exponential factor $$e^{-r/2a_0}$$ is never zero for finite $$r$$, and the constant prefactor is non-zero, the node must come from

$$2 - \frac{r}{a_0} = 0$$

Solving for $$r$$,

$$\frac{r}{a_0} = 2$$

Hence, $$r_0 = 2a_0$$. So, the answer is $$r_0 = 2a_0$$.

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

Solution

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