# Relative Sizes of Atomic Orbitals

## Atomic Orbital Shells

The size of a given orbital is primarily determined by the principal quantum number (n). The electrons in an atom can be viewed as residing in shells, the size of which is established by the principal quantum number.

(angstroms)
Nbr. Electrons
1 K s 1.4 2
2 L s, p 4.8 8
3 M s, p, d 10.3 18
4 N s, p, d, f 17.8 32

The third column of this table lists the radius of the isosurface for the corresponding s orbital containing 90% of the electron density.

As the size of the shell grows, the total number of electrons that can reside in the shell also increases.

The electrons in the outermost (largest) shell of an atom are called valence electrons. Electrons in the inner shells are called core electrons. When modeling chemical bonding, only valence electrons are considered.

Within each shell, electrons can exist in various subshells, labeled s, p, d, and f. These letters originate from visual characterizations of spectral lines for alkali metals by early spectroscopists: sharp, principal, diffuse, fundamental.

## Relative Sizes of Shells

Examine the radial distribution functions of the 1s, 2s and 3s orbitals, which are graphed at right. Use this graph to answer the following questions. For a different perspective, go to the bottom of this page and compare the 1s, 2s and 3s isosurfaces.

1. How does the size of the orbital vary as the value of n increases?

2. If an atoms has electrons in the K, L and M shells, is it necessary to consider the K and L shells when modeling chemical bonding? Why or why not?
Radial Distribution Plot of Hydrogen s Orbitals

## SubShells

Examine the radial distribution functions of the 4s, 4p, 4d and 4f orbitals, which are graphed at right. Use this graph to answer the following questions. For a different perspective, go to the bottom of this page and compare the 4s, 4p and 4d isosurfaces.

1. Which subshell simultaneously places electron density closest to the nucleus and furthest from the nucleus?

2. Computational chemistry indicates that, for a given shell, d orbitals are much less important than s and p orbitals in chemical bonding. Explain this results in terms of the radial distribution functions.

3. Chemists ignore f orbitals when describing chemical bonding. Is this reasonable?

Radial Distribution Plot of Hydrogen s Orbitals

In the viewer below, select various orbitals to compare their relative sizes. The isosurfaces provide a different way to visualize the size of orbitals than the radial distribution functions graphed above. Revisit the questions asked above using the isosurfaces to quide you to answers.

## Atomic Orbital Isosurfaces

AtomicOrbitals-Size.html version 3.0