The wavefunction of a 2s electron is given by -2s - 1-4 -2- 1-a03-2 2 - r-a0e-r-a0It has a node at r - r0- The value of r0-a0 is

Ψ^2 = 1/32 π^2 (1/a_0)^3 (2 r/a_0)^2 e^ 2r/a_0 When r = r_0, it has a node (i.e.) nbsp;ψ^2 = 0 1/32 π^2 (1/a_0)^3 (2 r_0/a_0)^2 e^ 2r_0/a_0= 0 From this r ...

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Byju's Answer

Standard XII

Physics

Potential Energy of a System of Multiple Point Charges

The wavefunct...

Question

The wavefunction of a 2s electron is given by $ψ_{2 s} = \frac{1}{4 \sqrt{2} π} (\frac{1}{a_{0}})^{\frac{3}{2}} (2 - \frac{r}{a_{0}}) e^{\frac{- r}{a_{0}}}$
It has a node at $r = r_{0}$ . The value of $\frac{r_{0}}{a_{0}}$ is___

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Solution

$ψ^{2} = \frac{1}{32 π^{2}} (\frac{1}{a_{0}})^{3} (2 - \frac{r}{a_{0}})^{2} e^{\frac{- 2 r}{a_{0}}}$
When $r = r_{0}$ , it has a node (i.e.) $ψ^{2} = 0$
$\frac{1}{32 π^{2}} (\frac{1}{a_{0}})^{3} (2 - \frac{r_{0}}{a_{0}})^{2} e^{\frac{- 2 r_{0}}{a_{0}}} = 0$
From this relation it is clear that any of these terms
$(i . e) \frac{1}{32 π^{2}} (o r) (\frac{1}{a_{0}})^{3} (o r) (2 - \frac{r_{0}}{a_{0}})^{2} (o r) (e^{\frac{- 2 r_{0}}{a_{0}}}$ ) has to be equal to zero.
It is only possible for $(2 - \frac{r_{0}}{a_{0}})$ to be equal to 0, all the others cannot ever become zero

Hence, $2 - \frac{r_{0}}{a_{0}} = 0 (o r) \frac{r_{0}}{a_{0}} = 2$

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Similar questions

Q. The wave function of

2 s

electron is given by :

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}})}

. If has a node at

r = r_{0}

, find relation between

r_{0}

and

a_{0}

Q. The wave function of 2s electrons is given by :

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}})}

If it has a node at

r = r_{0}

, then the relation between

r_{0}

and

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}})}^{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^{- 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

a_{0}

is given as

x a_{0} = r_{0}

, value of

x

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The wavefunction of a 2s electron is given by ψ2s=14√2π(1a0)32(2−ra0)e−ra0 It has a node at r=r0. The value of r0a0 is___

The wavefunction of a 2s electron is given by $ψ_{2 s} = \frac{1}{4 \sqrt{2} π} (\frac{1}{a_{0}})^{\frac{3}{2}} (2 - \frac{r}{a_{0}}) e^{\frac{- r}{a_{0}}}$
It has a node at $r = r_{0}$ . The value of $\frac{r_{0}}{a_{0}}$ is___