Answer to Question #70411 in Inorganic Chemistry for Hasibul islam

Question

How to proof d orbital is spherical by wave function in absence of magnetic field

Answer 1

The shape and symmetry of the orbitals are given by the orbital quantum numbers l and m: the s-orbitals are spherically symmetric, the p, d and f-orbitals have a more complex shape, defined by the angular parts of the wave function - angular functions. The angular functions Ylm (φ, θ) are the eigenfunctions of the squared angular momentum operator L², which depend on the quantum numbers l and m, are complex and describe in the spherical coordinates (φ, θ) the angular dependence of the probability of finding an electron in the central field of the atom. The linear combination of these functions determines the position of the orbitals relative to the Cartesian coordinate axes.