The wave function - of 2 s is given by-2 s -1-2 -2 -1- a 01-22- r - a 0 e - r - 2 a 0At r - r 0 radial node is formed- Thus for 2 s - r 0 in terms of a 0 is-A- r0-2 a0B- r0-a0-2C- r 0- a 0D- r 0-4 a 0

The correct option is A r_0 = 2a_0When r=r_0 , Ψ_2s=0 ∴ from the given equation: 2 ra_0 = 0 r=2a_0 Therefore, radial node is formed at 2a_0. ...

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Standard XII

Physics

RMS Value of Current in Sinusoidal AC

The wave func...

Question

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

r_{0} = a_{0}

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r_{0} = 2 a_{0}

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r_{0} = \frac{a_{0}}{2}

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r_{0} = 4 a_{0}

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Solution

The correct option is B $r_{0} = 2 a_{0}$
When $r = r_{0}$ , $Ψ_{2 s} = 0$
$∴$ from the given equation:
$2 - \frac{r}{a_{0}} = 0$
$r = 2 a_{0}$
Therefore, radial node is formed at $2 a_{0}$ .

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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^{- \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^{- \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 / 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^{(- 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 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 wave function (Ψ) of 2s is given by: Ψ2s=12√2π(1a0)12{2−ra0}e−r/2a0 At r=r0 radial node is formed. Thus for 2s, r0 in terms of a0 is:

The correct option is B r0=2a0When r=r0 , Ψ2s=0 ∴ from the given equation: 2−ra0=0 r=2a0 Therefore, radial node is formed at 2a0.

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

The correct option is B $r_{0} = 2 a_{0}$
When $r = r_{0}$ , $Ψ_{2 s} = 0$
$∴$ from the given equation:
$2 - \frac{r}{a_{0}} = 0$
$r = 2 a_{0}$
Therefore, radial node is formed at $2 a_{0}$ .