structure and bonding: electrons as a wave

electron in 1 dimension

• confined in 1 dimensional box

• walls of box have infinite negative potential energy and there is 0 potential energy inside the box

• walls are infinitely repulsive so electron cannot be at walls

• atomic orbital described in terms of quantum numbers: 1 dimension = 1 quantum number

• most likely in the middle of box

electron is a wave

must be continuous and have 0 amplitude

locus

point at which the wavelength crosses 0

Born interpretation

• wavelength squared is the probability of finding the electron at that point

electron waves in 2 dimensions

• confined in a 2 dimensional box

• most likely to be ¼ or ¾ of the way through the box

• energy levels are doubly degenerate in square box

electron on a ring

• electron confined to 2D ring of radius R

• the ring has 0 potential energy but surrounding area has infinite potential energy - electron cannot leave ring