Question

b. Briefly explain the differences between a boundary surface and the radial distribution function for hydrogenic atoms.

Answer 1

(a) Boundary surface is a common way of representing atomic orbitals, incorporating the volume in which there is about a 90% probability of finding the electron at a given time. The boundary surface is a closed surface or a set of closed surfaces, such that there is 90% chance that an electron is interior and a 10% that the electron is exterior of the closed surface.

In short, boundary surface for a hydrogenic orbital is drawn so as to contain 90% of the probability density of an electron in that orbital and its shape varies from orbital to orbital as the electron density distribution is different for different orbitals.

(b) The radial distribution function tells the probability that an electron will be found anywhere within a shell of radius (r) around the nucleus. It provides a better picture of where the electron is probably to be found with respect to nucleus than the probability density (the square of the wavefunction is the probability density).