The radial probability density of a hydrogen wavefunction in the 1s state is given by P (r) = |4ar² (R1s(r))²i and the radial wavefunction R1, (r) = , where ao is the Bohr radius. Using the standard integral * " e-kz dæ = calculate the standard deviation in the radial position from the nucleus for the 1s state in the Hydrogen atom. Give your answer in units of the Bohr radius ag.

Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter8: Quantum Mechanics In Three Dimensions
Section: Chapter Questions
Problem 22P
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The radial probability density of a hydrogen wavefunction in the 1s state is given by P (r) = |47r² (R1s(r))²|
, where ao is the Bohr radius. Using the standard integral
and the radial wavefunction R1, (r) =
z e ,
3/2
z" e-k dæ = , calculate the standard deviation in the radial position from the nucleus for the 1s state in
the Hydrogen atom. Give your answer in units of the Bohr radius ao.
Transcribed Image Text:The radial probability density of a hydrogen wavefunction in the 1s state is given by P (r) = |47r² (R1s(r))²| , where ao is the Bohr radius. Using the standard integral and the radial wavefunction R1, (r) = z e , 3/2 z" e-k dæ = , calculate the standard deviation in the radial position from the nucleus for the 1s state in the Hydrogen atom. Give your answer in units of the Bohr radius ao.
Expert Solution
Step 1

We have the wave function given by R(r)=π-1/2ao-3/2e-r/ao and radial probability density P(r)=|4πr2R2(r)| where ao is the Bohr radius. 

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