The wave function (Ψ) of 2 s -orbital is given by Ψ2 s=(1/2 √32 π) ⋅[(1/a0)]3 / 2[2-(r/a0)] e-r / 2 a0 At r=r0, radial node is formed. The ratio of r0: a0 is .

Question

The wave function (Ψ) of 2 s -orbital is given by Ψ2 s=(1/2 √32 π) ⋅[(1/a0)]3 / 2[2-(r/a0)] e-r / 2 a0 At r=r0, radial node is formed. The ratio of r0: a0 is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Ψ2 s =(1/2 √32 π) ⋅[(1/a0)]-3 / 2 ⋅[2-(r/a0)] ⋅ e-r / 2 a0 For radial node at r=r0, ψ2 s2=0 . This is possible only when [2-(r0/a0)]=0 or 2=(r0/a0)

Q. The wave function $(Ψ)$ of $2 s$ -orbital is given by
$Ψ_{2 s} = \frac{1}{2 32 π} \cdot [\frac{1}{a _{0}}]^{3/2} [2 - \frac{r}{a _{0}}] e^{- r /2 a_{0}}$
At $r = r_{0},$ radial node is formed. The ratio of $r_{0} : a_{0}$ is _______.

$Ψ_{2 s} = \frac{1}{2 32 π} \cdot [\frac{1}{a _{0}}]^{- 3/2} \cdot [2 - \frac{r}{a _{0}}] \cdot e^{- r /2 a_{0}}$

For radial node at $r = r_{0}, ψ_{2 s}^{2} = 0.$

This is possible only when

$[2 - \frac{r _{0}}{a _{0}}] = 0$ or $2 = \frac{r _{0}}{a _{0}}$

Q. The wave function (Ψ) of 2s -orbital is given by Ψ2s​=232π​1​⋅[a0​1​]3/2[2−a0​r​]e−r/2a0​ At r=r0​, radial node is formed. The ratio of r0​:a0​ is _______.

Ψ2s​=232π​1​⋅[a0​1​]−3/2⋅[2−a0​r​]⋅e−r/2a0​ For radial node at r=r0​,ψ2s2​=0. This is possible only when [2−a0​r0​​]=0 or 2=a0​r0​​

Q. The wave function $(Ψ)$ of $2 s$ -orbital is given by
$Ψ_{2 s} = \frac{1}{2 32 π} \cdot [\frac{1}{a _{0}}]^{3/2} [2 - \frac{r}{a _{0}}] e^{- r /2 a_{0}}$
At $r = r_{0},$ radial node is formed. The ratio of $r_{0} : a_{0}$ is _______.

$Ψ_{2 s} = \frac{1}{2 32 π} \cdot [\frac{1}{a _{0}}]^{- 3/2} \cdot [2 - \frac{r}{a _{0}}] \cdot e^{- r /2 a_{0}}$

For radial node at $r = r_{0}, ψ_{2 s}^{2} = 0.$

This is possible only when

$[2 - \frac{r _{0}}{a _{0}}] = 0$ or $2 = \frac{r _{0}}{a _{0}}$