The wave function (Ψ) of 2 s is given by Ψ2 n =(1/2 √2 π)((1/a0))1 / 2(2-(r/a0)) e-(r/2 a0) At r=r0, radial node is formed. Thus, r0 in terms of a0

Question

The wave function (Ψ) of 2 s is given by Ψ2 n =(1/2 √2 π)((1/a0))1 / 2(2-(r/a0)) e-(r/2 a0) At r=r0, radial node is formed. Thus, r0 in terms of a0 (A) r0=(a0/2) (B) r0=2 a0 (C) r0=4 a0 (D) r0=a0

Tardigrade Admin · Accepted Answer

At node Ψ2 s=0 ∴ 2-(r0/a0)=0 ∴ r0=2 a0

Q. The wave function $(Ψ)$ of $2 s$ is given by
$Ψ_{2 n} = \frac{1}{2 2 π} (\frac{1}{a _{0}})^{1/2} (2 - \frac{r}{a _{0}}) e^{- \frac{r}{2 a _{0}}}$
At $r = r_{0}$ , radial node is formed. Thus, $r_{0}$ in terms of $a_{0}$

$r_{0} = \frac{a _{0}}{2}$

$r_{0} = 2 a_{0}$

$r_{0} = 4 a_{0}$

$r_{0} = a_{0}$

At node $Ψ_{2 s} = 0$
$∴ 2 - \frac{r _{0}}{a _{0}} = 0$
$∴ r_{0} = 2 a_{0}$

Q. The wave function (Ψ) of 2s is given by Ψ2n​=22π​1​(a0​1​)1/2(2−a0​r​)e−2a0​r​ At r=r0​, radial node is formed. Thus, r0​ in terms of a0​

r0​=2a0​​

r0​=2a0​

r0​=4a0​

r0​=a0​