The wave function (ψ) of 2s is given by 42s=122π(1a0)1/2[2−ra0]e−r/2a0At r=r0, radial node is formed.Calculate ro in terms of ao

ψ2s2=0 for radial node r=r0 (2−ra0)=0 2=r0a0⇒r0=2a0

The wave function (ψ) of 2s is given by 42s=122π(1a0)1/2[2−ra0]e−r/2a0At r=r0, radial node is formed.Calculate ro in terms of ao

ψ2s2=0 for radial node r=r0 (2−ra0)=0 2=r0a0⇒r0=2a0

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The wave function $(ψ)$ of 2s is given by
$4_{2 s} = \frac{1}{2 \sqrt{2} π} {(\frac{1}{a_{0}})}^{1 / 2} [2 - \frac{r}{a_{0}}] e^{- r / 2 a_{0}}$
At $r = r_{0},$ radial node is formed.
Calculate $r_{o}$ in terms of $a_{o}$

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$2 a_{0}$

$a_{0} / 2$

$\frac{a_{0}}{2 \sqrt{2}}$

$2 \sqrt{2} a_{0}$

answer is A.

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Detailed Solution

$ψ_{2 s}^{2} = 0$ for radial node $r = r_{0}$
$(2 - \frac{r}{a_{0}}) = 0$ $2 = \frac{r_{0}}{a_{0}} \Rightarrow r_{0} = 2 a_{0}$

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The wave function (ψ) of 2s is given by 42s=122π(1a0)1/2[2−ra0]e−r/2a0At r=r0, radial node is formed.Calculate ro in terms of ao

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The wave function $(ψ)$ of 2s is given by
$4_{2 s} = \frac{1}{2 \sqrt{2} π} {(\frac{1}{a_{0}})}^{1 / 2} [2 - \frac{r}{a_{0}}] e^{- r / 2 a_{0}}$
At $r = r_{0},$ radial node is formed.
Calculate $r_{o}$ in terms of $a_{o}$