JEE MAIN - Chemistry (2023 - 30th January Evening Shift - No. 14)
The wave function $(\Psi)$ of $2 \mathrm{~s}$ is given by
$$ \Psi_{2 \mathrm{~s}}=\frac{1}{2 \sqrt{2 \pi}}\left(\frac{1}{a_0}\right)^{1 / 2}\left(2-\frac{r}{a_0}\right) e^{-r / 2 a_0} $$
At $r=r_0$, radial node is formed. Thus, $r_0$ in terms of $a_0$
$$ \Psi_{2 \mathrm{~s}}=\frac{1}{2 \sqrt{2 \pi}}\left(\frac{1}{a_0}\right)^{1 / 2}\left(2-\frac{r}{a_0}\right) e^{-r / 2 a_0} $$
At $r=r_0$, radial node is formed. Thus, $r_0$ in terms of $a_0$
$r_0=a_0$
$r_0=4 a_0$
$r_0=2 a_0$
$r_0=\frac{a_0}{2}$
Explanation
For radial node $${\psi _{2s}} = 0$$
$$\therefore$$ $$r = 2{a_0}$$
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