Explore BrainMass
Share

The Hydrogen Atom and the Radial Angular Momentum

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Hydrogen atom
The radial probability density for an electron is r2R2(r). That means that the probability of finding an electron at a certain radius r within a radial thickness dr is dr* r2R2(r) for an infinitely thin shell and approximately r* r2avg R2(ravg) for a shell of finite thickness r.
The quantity ravg is some average radius within the shell...

(a) Estimate the probability that an electron in the n=1,l=0 state will be found in the region from r=0m to r= 10-15m.

(b) Repeat the calculation for n=2, l=1.

(c) Compare the two results, explain their difference, and explain the relevance of 10-15m distance from the center of the atom.

(d) Consider the state n=2, l=0 in hydrogen. What are the values of r for which the probability density is zero?
Sketch the probability density as a function of r for this state.

© BrainMass Inc. brainmass.com October 16, 2018, 11:05 pm ad1c9bdddf
https://brainmass.com/physics/angular-momentum/the-hydrogen-atom-radial-angular-momentum-245596

Solution Summary

The solution examines a hydrogen atom and the radial angular momentum. The probability that an electron in the n=1 and I=0 state will be found in the region from r=0m to r=10-15m is determined.

$2.19
Similar Posting

Angular Momentum Quantum Numbers

Define the quantum numbers required to specify the state of an electron in hydrogen. The spatial part of the wave function describing a particular hydrogen atom has no angular dependence. Give the values of all the angular momentum quantum numbers for the electron.

View Full Posting Details