Instant Notes: Analytical Chemistry

absorption spectrum. It must be noted, however, that when a large change

occurs (e.g. due to an alteration in the electronic structure of a molecule) the less

energetic changes, such as the vibration of bonds and rotation of the molecule,

will happen as well, leading to more complex spectra.

Quantum theory shows that atoms exist only in discrete states, each of which

possesses a characteristic energy, defined by quantum numbers, which charac-

terize the atomic state. Transitions may occur only between these levels, and

even then some transitions are unfavorable. Electrons occupy atomic orbitals

with characteristic spatial distributions around the nucleus.

The discrete energy levels arise naturally as the allowed solutions of the wave

equations for the system under consideration. Electronic energy levels in atoms

may be accounted for by solving the Schrödinger wave equation.

Atoms have electronic energy levels and atomic orbitals that are defined by

three quantum numbers that can have integer values:

n principal quantum number,

l orbital angular momentum quantum number,

m magnetic quantum number, and

ms electronic spin quantum number which can be +1/2 or -1/2 only.

The energy of an orbital is mostly dependent on its principal quantum number

n. In fact, for hydrogen, the energy depends only on n. There are only certain

allowed values of the other quantum numbers. For example, l may take integer

values from 0 to (n– 1); m values from +l to -land ms+1/2 or –1/2.

The different orbitals are described by symbols:

s (sharp) for l = 0

p (principal) for l = 1

d (diffuse) for l= 2

f ( fundamental) for l = 3

For atoms other than hydrogen, the other quantum numbers modify the energy

slightly. For example, the 3p level where n =3, l =1 has a higher energy than the

3 s with n =3, l =0. These are often referred to as subshells.

The atoms of the various elements are built up by adding electrons into the

next empty level with the lowest energy, remembering that each level may

Atomic energy
levels

E1 – Electromagnetic radiation and energy levels 191

Table 2. The regions of the electromagnetic spectruma

Wavelength range Frequency (Hz) Region Spectra

100–1 m 3–300 ¥ 106 Radiofrequency Nuclear magnetic resonance
1–0.1 m 0.3–3 ¥ 109 Radiofrequency Electron spin resonance
100–1 mm 3–300 ¥ 109 Microwave Rotational
1–0.02 mm 0.3–15 ¥ 1012 Far infrared Vibrational
20–2 mm 15–150 ¥ 1012 Infrared (IR) Vibrational
2–0.8 mm 150–375 ¥ 1012 Near infrared Vibrational
800–400 nm 375–750 ¥ 1012 Visible Electronic
400–150 nm 750–2000 ¥ 1012 Ultraviolet (UV) Electronic
150–2 nm 2–150 ¥ 1015 Vacuum UV Electronic
2–0.1 nm 150–3000 ¥ 1015 X-ray Inner shell electronic
0.1–0.0001 nm 3–3000 ¥ 1018 g-ray Nuclear reactions

aThe regions overlap considerably, and the range is approximate.