Question

Spherical Harmonics

The spherical harmonic,(on photo) is the solution that we have labelled the 3rd orbital for the hydrogen atom

At what values of theta does this function have nodes?

Are the nodes points, lines, planes, or other surfaces? Explain how you areived at your answer.

The spherical harmonie, yr( (30sY-1) is the solution that we have labelled the 3d, orbital for the hydrogen atom for s) 1) At what values of 8 does this function have nodes? 2) Are the nodes points, lines, planes, or other surfaces? Explain how you arrived at your answer.

Answer 1

"Given spherical Harmonics upsilon^0_2 (theta, emptyset) = squareroot 5/6 pi (3 cos theta - 1) (1) At Node wave function must be zero upsilon^0_2 (theta, emptyset) = 0 rightdoublearrow 3 cos^2 theta - L = 0 cos^2 theta = 1/ squareroot 3 cos theta = plusminus 1/ squareroot 3 theta = 55 degree (2) In spherical polar co - ordinate we know that theta = constant Represent surface ""Cone"" Hence Node theta = 55 degree Represent cone surface"