The wave function (Ψ) of 2s is given by Ψ _ 2s = 1 2 2π ( 1 a _ 0 )...

The wave function ($Ψ$) of 2s is given by,

${Ψ}_{2s} = \dfrac{1}{2\sqrt{2\pi}}{\left(\dfrac{1}{{a}_{0}}\right)}^{1 / 2}\left(2 - \dfrac{r}{{a}_{0}}\right){e}^{- r / 2{a}_{0}}$

At $r = {r}_{0}$, radial node is formed.

${{Ψ}_{2s}}^{2}$= Probability density of finding an electron

At node, ${{Ψ}_{2s}}^{2} = 0$ ($∵$Probability of finding an electron is zero at the node)

${{Ψ}_{2s}}^{2} = {\left[\dfrac{1}{2\sqrt{2\pi}}{\left(\dfrac{1}{{a}_{0}}\right)}^{1 / 2}\left(2 - \dfrac{r}{{a}_{0}}\right){e}^{- r / 2{a}_{0}}\right]}^{2}$

$⇒ 0 = \dfrac{1}{8\pi}\left(\dfrac{1}{{a}_{0}}\right){\left(2 - \dfrac{{r}_{0}}{{a}_{0}}\right)}^{2}{e}^{- 2{r}_{0} / {a}_{0}}$

$⇒ \left[2 - \dfrac{{r}_{0}}{{a}_{0}}\right] = 0$

$⇒ 2 = \dfrac{{r}_{0}}{{a}_{0}}$

$⇒ 2{a}_{0} = {r}_{0}$

So, the correct option is D.