What may be the correct orbital notation if the wave function is -1-81 -6 -1-a0 3-2- e -33 cos 2-1 - Here - r - a 0 and a 0- h 2- 0- 2A- 4 sB- 2 pxC- 3 pyD- 3 d z 2

The correct option is D 3d_z^2 Ψ=0 if cos^2 θ=1/3 ⇒ cosθ=±1/√(3) So there are two angular nodes for this orbital hence l=2 i.e. orbital should be 3d_z^2. nbs ...

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Standard XII

Physics

Huygens' Principle

What may be t...

Question

What may be the correct orbital notation if the wave function is
$- Ψ = \frac{1}{81 \sqrt{6 π}} (\frac{1}{a_{0}}) \frac{3}{2} σ e^{\frac{σ}{3}} (3 c o s^{2} θ - 1); H e r e σ = r / a_{0} a n d a_{0} = \frac{h^{2} ϵ_{0}}{π m e^{2}}$

4 s

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2 p_{x}

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3 p_{y}

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3 d_{z}^{2}

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Solution

The correct option is D $3 d_{z}^{2}$
$- Ψ$ =0 if $c o s^{2} θ = \frac{1}{3} \Rightarrow c o s θ = \pm \frac{1}{\sqrt{3}}$
So there are two angular nodes for this orbital hence
l=2 i.e. orbital should be $3 d_{z}^{2}$ .

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Similar questions

Q. What may be the correct orbital notation if the wave function is

- Ψ = \frac{1}{81 \sqrt{6 π}} (\frac{1}{a_{0}}) \frac{3}{2} σ e^{\frac{σ}{3}} (3 c o s^{2} θ - 1); H e r e σ = r / a_{0} a n d a_{0} = \frac{h^{2} ϵ_{0}}{π m e^{2}}

Q. The Schrodinger wave function for Hydrogen atom of 4s orbital is given by:

Ψ_{4 s} = \frac{1}{16 \sqrt{3}} {(\frac{1}{a_{0}})}^{\frac{3}{2}} [(σ - 1) (σ^{2} - 8 σ + 12)] e^{- σ / 2}

where

a_{0}

1^{s t}

Bohr radius and

σ = \frac{2 r}{a_{o}}

.

The distance from the nucleus where there is no radial node will be:

Q. The radial wave function of an orbital is

2 {(\frac{Z}{a_{0}})}^{\frac{3}{2}} e^{\frac{Z r}{- a_{0}}}

for

H -

atom. The wave function is for: (notations have their usual meaning)

Q. The wave function for an orbital is

H -

atom is given as:

Ψ = (\frac{\sqrt{2}}{81 \sqrt{π}}) {(\frac{1}{a_{0}})}^{\frac{2}{3}} (6 - \frac{r}{a_{0}}) {(\frac{r}{a_{0}})}^{- \frac{r}{3 a_{0}}} . sin θ sin ϕ

The orbital is:

Q. The complete wave function of an orbital of hydrogen is given as

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

,
(

a_{0}

is first Bohr radius)
Which of the following option(s) is/are correct?

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What may be the correct orbital notation if the wave function is −Ψ=181√6π(1a0)32 σeσ3(3cos2θ−1);Here σ=r/a0 and a0=h2ϵ0πme2

The correct option is D 3d2z−Ψ=0 if cos2 θ=13⇒cosθ=±1√3 So there are two angular nodes for this orbital hence l=2 i.e. orbital should be 3d2z.

What may be the correct orbital notation if the wave function is
$- Ψ = \frac{1}{81 \sqrt{6 π}} (\frac{1}{a_{0}}) \frac{3}{2} σ e^{\frac{σ}{3}} (3 c o s^{2} θ - 1); H e r e σ = r / a_{0} a n d a_{0} = \frac{h^{2} ϵ_{0}}{π m e^{2}}$

The correct option is D $3 d_{z}^{2}$
$- Ψ$ =0 if $c o s^{2} θ = \frac{1}{3} \Rightarrow c o s θ = \pm \frac{1}{\sqrt{3}}$
So there are two angular nodes for this orbital hence
l=2 i.e. orbital should be $3 d_{z}^{2}$ .