5 Steps to a 5 AP Chemistry 2019

Spectroscopy, Light, and Electrons ❮ 141

Atomic Orbitals

Bohr’s model worked well for hydrogen, the simplest atom, but didn’t work very well for

any others. In the early 1900s, Schrödinger developed a more involved model and set of

equations that better described atoms by using quantum mechanical concepts. His model

introduced a mathematical description of the electron’s motion called a wave function or

atomic orbital. Squaring the wave function (orbital) gives the volume of space in which

the probability of finding the electron is high. This is commonly referred to as the electron

cloud.

Schrödinger’s equation required the use of three quantum numbers to describe each

electron within an atom, corresponding to the orbital size, shape, and orientation in space.

It was also found that a quantum number concerning the spin of the electron was needed.

The first quantum number is the principal quantum number (n). It describes the

energy (related to size) of the orbital and relative distance from the nucleus. The allowed

(by the mathematics of the Schrödinger equation) values are positive integers (1, 2, 3, 4,

etc.). The smaller the value of n, the closer the orbital is to the nucleus. The number n

is sometimes called the atom’s shell.

The second quantum number is the angular momentum quantum number (l). Its

value is related to the principal quantum number and has allowed values of 0 up to (n - 1).

For example, if n = 3, then the possible values of l would be 0, 1, and 2 (3 - 1). This

value of l defines the shape of the orbital:

● If l = 0, the orbital is called an s orbital and has a spherical shape with the nucleus at the

center of the sphere. The greater the value of n, the larger the sphere.

● If l = 1, the orbital is called a p orbital and has two lobes of high electron density on

either side of the nucleus. This makes for an hourglass or dumbbell shape.

● If l = 2, the orbital is a d orbital and can have variety of shapes.

● If l = 3, the orbital is an f orbital, with more complex shapes.

Figure 10.3, on the next page, shows the shapes of the s, p, and d orbitals. These are

sometimes called sublevels or subshells.

The third quantum number is the magnetic quantum number (ml). It describes

the orientation of the orbital around the nucleus. The possible values of ml depend on

the value of the angular momentum quantum number, l. The allowed values for ml are

• l through zero to +l. For example, for l = 2 the possible values of ml would be -2, -1,
  0, +1, +2. This is why, for example, if l = 1 (a p orbital), then there are three p orbitals
  corresponding to ml values of -1, 0, +1. This is also shown in Figure 10.3.
  The fourth quantum number, the spin quantum number (ms), indicates the direc-
  tion the electron is spinning. There are only two possible values for ms, +^1 ⁄ 2 and -^1 ⁄ 2.
  The quantum numbers for the six electrons in carbon would be:

QUANTUM FIRST SECOND THIRD FOURTH FIFTH SIXTH

NUMBER ELECTRON ELECTRON ELECTRON ELECTRON ELECTRON ELECTRON

n 1 1 2 2 2 2
l 0 0 0 0 1 1
ml 0 0 0 0 1 0
ms +^1 ⁄ 2 -^1 ⁄ 2 +^1 ⁄ 2 -^1 ⁄ 2 +^1 ⁄ 2 +^1 ⁄ 2

Therefore, the electron configuration of carbon is 1s^2 2s^2 2p^2.

ENRICHMENT