Knowledge of the probable locations of electrons in atoms (and in molecules) is fundamental to understanding their properties, and it is important to be able to interpret their wavefunctions.

Suppose the electron is in a 1s-orbital of a hydrogen atom. What is the probability of finding the electron in a small region a distance a₀ from the nucleus relative to the probability of finding it in the same small region located right at the nucleus?

ANTICIPATE You should expect a lower probability because the wavefunction decays exponentially with distance from the nucleus.

PLAN Compare the probability densities at the two locations. To do that, take the ratio of the squares of the wavefunction at the two locations. Because the probability density is independent of angle when l = 0, as remarked in the text, write the wavefunction simply as ψ(r) rather than as the more complete expression ψ(r,θ,ϕ).