Question

What is an example of an electron orbital practice problem?

Answer 1

I think you meant atomic orbital. Electrons aren't a class of orbitals, and there is no such thing as an orbital belonging to an electron.

1. Determine the number of orbitals in a theoretical subshell in which `l = 5`. (Hint: it corresponds to `m_l = 0, 1, . . . , pml`) What letter might correspond to this orbital subshell? Recall that the orbital lettering goes alphabetically after `f`.
2. Look up a radial distribution graph of the `2s` atomic orbital, and determine how many `a_0` from the center of the orbital can you never find an electron, ever (except for `r = 0` and `r -> oo`).
3. How many nodes does a `3d` orbital have? Show that it is `2`. What is the relationship between the `n` and the total number of nodes in general? Which are angular and which are radial nodes? Recall that the number of radial nodes is `n - l - 1`.

Answers:

1. `color(white)("h, because it goes s, p, d, f, g, h where "l = 5.`
   `color(white)("There are 2*5+1 = 11 orbitals in this subshell.")`
2. `color(white)("2a"_0)`
3. `color(white)(n - 1 "tells you how many total nodes there")`
   `color(white)("are in general, so there are no radial nodes"`
   `color(white)("because " n - l - 1 = 0. "So we know that"`
   `color(white)(n - 1 = 2.)`