The wave function - of 2s-orbitals given by- -2s-1-32-1a0-3-2-2-ra0-e-r-2a0at r-r0-radial node is formed-If r0 - xa0- find the value of x-

ψ_2s=1√(32π)[1a_0]^3/2[2 ra_0]e^ r/2a_0 For radial node at r=r_0, ψ^2_2s=0 . This is possible only when [2 r_0a_0]=0 #160; ∴ r_0=2a_0 ...

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Shapes of Orbitals and Nodes

The wave func...

Question

The wave function $(ψ)$ of $2 s$ -orbitals given by:
$ψ_{2 s} = \frac{1}{\sqrt{32 π}} {[\frac{1}{a_{0}}]}^{3 / 2} [2 - \frac{r}{a_{0}}] e^{- r / 2 a_{0}}$
at $r = r_{0}$ ,radial node is formed.If $r_{0}$ = $x a_{0}$ , find the value of $x$ .

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(Ψ)

2 s

Ψ_{2 s} = \frac{1}{2 \sqrt{2 π}} {(\frac{1}{a_{0}})}^{1 / 2} {2 - \frac{r}{a_{0}}} e^{- r / 2 a_{0}}

r = r_{0}

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(Ψ)

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Ψ_{2 s} = \frac{1}{2 \sqrt{2 π}} {(\frac{1}{a_{0}})}^{\frac{1}{2}} {2 - \frac{r}{a_{0}}} e^{- \frac{r}{2 a_{0}}}

r = r_{0}

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(Ψ)

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Ψ_{2 s} = \frac{1}{2 \sqrt{2 π}} {(\frac{1}{a_{0}})}^{\frac{1}{2}} {2 - \frac{r}{a_{0}}} e^{(- r / a_{0})}

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(Ψ)

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Ψ_{2 s} = \frac{1}{2 \sqrt{2 π}} {(\frac{1}{a_{0}})}^{\frac{1}{2}} {2 - \frac{r}{a_{0}}} e^{- r / 2 a_{0}}

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Ψ (2 s) = \frac{1}{4 \sqrt{2 π}} {(\frac{1}{a_{0}})}^{3 / 2} (2 - \frac{r}{a_{0}}) e^{(2 - \frac{r}{a_{0}})}

r = r_{0}

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