Log In Start studying!
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q. 31

Expert-verified
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1207

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

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

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 radial wave function is

The probability density is

The prob(in at )

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

Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.