Q. 31

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Found in: Page 1207

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# For an electron in the state of hydrogen, what is the probability of being in a spherical shell of thickness at distance (a) , (b) , and (c) from the proton?

(a) For an electron in the state of hydrogen, what is the probability of being in a spherical shell of thickness at distance is .

(b) For an electron in the state of hydrogen, what is the probability of being in a spherical shell of thickness at distance is .

(c) For an electron in the state of hydrogen, what is the probability of being in a spherical shell of thickness at distance is .

See the step by step solution

## Part (a) Step 1 : Given Information

We have given an electron in the state of hydrogen,

We have to find the probability of being in a spherical shell of thickness at distance of .

## Part (a) Step 2 : Simplification

We know that , the radial wave function of hydrogen in the state is

and the probability density is

The radial wave function and probability density for is

The probability is

Prob(in at )

The probability of being in a spherical shell of thickness at distance of is .

## Part (b) Step 1 : Given Information

We have given an electron in the state of hydrogen,

We have to find the probability of being in a spherical shell of thickness at distance of

## Part (b) Step 2 : Simplification

Likewise,

The radial wave function for is

The probability density for is

The prob(in at r)

The probability of being in a spherical shell of thickness at distance of is

## Part (c) Step 1 : Given Information

We have given an electron in the state of hydrogen,

We have to find the probability of being in a spherical shell of thickness at distance of

## Part (c) Step 2 : Simplification

For ,

The probability density is

The prob(in at )

The probability of being in a spherical shell of thickness at distance of is