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Standard XII

Chemistry

Shapes of Orbitals and Nodes

The wave func...

Question

The wave function $(Ψ)$ of $2 s$ is given by:
$Ψ_{2 s} = \frac{1}{2 \sqrt{2 π}} {(\frac{1}{a_{0}})}^{\frac{1}{2}} {2 - \frac{r}{a_{0}}} e^{(- r / a_{0})}$
Where $a_{0}$ is Bohr's radius. If the radial node in $2 s$ is at $r_{0},$ then find $r_{0}$ in terms of $a_{0}$ .

a_{0}

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2 a_{0}

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3 - (5)^{\frac{1}{2}} a_{0}

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None of these

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Solution

The correct option is B $2 a_{0}$
$ψ_{2 s}^{2} =$ Probability density of finding electron
$ψ_{2 s}^{2} = 0$ (at node)
( $∵$ probability of finding an electron is zero at the node)
$∴ 0 = \frac{1}{8 π} (\frac{1}{a_{0}}) {(2 - \frac{r_{0}}{a_{0}})}^{2} e^{(\frac{- 2 r_{0}}{a_{0}})}$
(squaring the given value of $ψ_{2 s}$ )
or $[2 - \frac{r_{0}}{a_{0}}] = 0; ∴ 2 = \frac{r_{0}}{a_{0}}; 2 a_{0} = r_{0}$

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Similar questions

Q. The wave function

(Ψ)

2 s

is given by:

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})}

Where

a_{0}

is Bohr's radius. If the radial node in

2 s

is at

r_{0},

then find

r_{0}

in terms of

a_{0}

Q. The wave function

(Ψ)

2 s

is given by:

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}

, radial node is formed. Thus for

2 s

r_{0}

in terms of

a_{0}

is:

Q. The wave function

(Ψ)

2 s

is given by:

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}}

r = r_{0}

radial node is formed. Thus for

2 s

r_{0}

in terms of

a_{0}

is:

Q. The wave function

(Ψ)

2 s

is given by:

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}

, radial node is formed. Thus for

2 s

r_{0}

in terms of

a_{0}

is:

Q. The Schrondinger equation for hydrogen atom is

ψ = \frac{1}{4 \sqrt{2 π}} (\frac{1}{a_{0}})^{\frac{3}{2}} (2 - \frac{r_{0}}{a_{0}}) e^{-} \frac{r_{0}}{a_{0}}

, where

a_{0}

is Bohr's radius. If the radial node is

2 s

be at

r_{0}

.
Then,

r_{0}

in terms of

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is given as

x a_{0} = r_{0}

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Shapes of Orbitals and Nodes

Standard XII Chemistry

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The wave function (Ψ) of 2s is given by: Ψ2s=12√2π(1a0)12{2−ra0}e(−r/a0) Where a0 is Bohr's radius. If the radial node in 2s is at r0, then find r0 in terms of a0.

The correct option is B 2a0ψ22s= Probability density of finding electron ψ22s=0 (at node) (∵ probability of finding an electron is zero at the node) ∴0=18π(1a0)(2−r0a0)2e(−2r0a0) (squaring the given value of ψ2s) or [2−r0a0]=0;∴2=r0a0;2a0=r0

The wave function $(Ψ)$ of $2 s$ is given by:
$Ψ_{2 s} = \frac{1}{2 \sqrt{2 π}} {(\frac{1}{a_{0}})}^{\frac{1}{2}} {2 - \frac{r}{a_{0}}} e^{(- r / a_{0})}$
Where $a_{0}$ is Bohr's radius. If the radial node in $2 s$ is at $r_{0},$ then find $r_{0}$ in terms of $a_{0}$ .