Question

Define grerade and increase orbits. Classify the following orbitals as gerade or ungerade.
I- 1s ii- 2px iii- 3dxy

Answer 1

Orbitals which are left unchanged by the operation of inversion (are symmetric) are gerade, while those which undergo a change in sign (are antisymmetric) are ungerade.

(i) 1s - gerade

S orbitals are spherically symmetric. There is no change in the sign of wave furnction throught the inversion operation (center of inversion is in the center of the sphere).

(ii) 2px - ungerade.

P orbitals are dumbbell chaped. One lobe has negative sign, the other has positive sign. There is change in sign of wave function throught operation of inversion (center of inversion is in the origin)

(iii) 3dxy -gerade

d orbital is dumbbell shaped. There are four lobes. Each two lobes that are opposite one another are of the same sign. There is no change in the sign of wave furnction throught the inversion operation (center of inversion is in the origin).