Q. 31

Expert-verifiedFound in: Page 1207

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 .

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 .

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 .

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

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

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

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 is94% of StudySmarter users get better grades.

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