# The Hydrogen Atom and the Radial Angular Momentum

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.

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.

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