If we are to make sense of the bonding between atoms, it seems that me must accept that the electrons around an atom do not just exist in an arbitrary heap or in any random orbital, but must somehow be structured. This structure should allow us to make sense of why some electrons are easier to remove than others, and why only a certain number of bonds can form around a given atom by "sharing " electrons".

It is likely that you have encountered this notion of electron structure in other courses where you were taught that electrons exist in shells called energy levels. Direct evidence for such shells comes from exploring the interaction of light with atoms. To help make sense of this evidence we will start by considering some properties of light.

Light can be thought of as a wave that moves through space at a set speed â€“ 3.00 x 10^{8} m/s. Although all types of light have this speed in common, they differ in their wavelength and frequency. The **wavelength** of a wave is the distance between corresponding points in a wave. Any two corresponding points can be chosen to determine the wavelength. Three pairs of such corresponding points are shown below.

The crest of the wave depicted above has a wavelength of 3.00 x 10^{8} m. All light has a velocity of 3.00 x 10^{8} m/s, so it would required one second to get from the points A and B shown. At a particular point, say point B, one crest of the wave would pass every second and we say that the frequency of the wave is 1 wave every second. (The units for frequency are written as waves/s, 1/s, or Hz).

Frequency and wavelength are inversely proportional. Consider the two waves shown above. The wavelength of the blue wave is twice that of the red. To travel at the same speed, the crest of the red wave will pass at a given point more frequently than the blue - 2 times as often. In the wave shown above, the short red wave, that is half as long , will pass a given point 2 times as often. We say the frequency of the red wave is 2 times as large as that of the blue wave.

We can write this relationship in the form of an equation.

$$ \color{black} c = \lambda \nu $$

c = 3.00 × 10^{8} m/s

λ = wavelength in meters

ν = frequency in 1/s or Hz

**Example 1:** What is the freqeuncy of a wave that has a wavelength of 4.50 × 10^{-7} m?
\begin{align*}
c & = \lambda \nu \\\\
\nu & = \frac {c}{\lambda } \\\\
\nu & = \frac {3.00 \times 10^8 \, \frac{m}{s}}{4.50 \times 10^{-7} \, m } \\\\
\nu & = 6.67 \times 10^{14} \, \frac{1}{s}
\end{align*}

We are using the term light to include all types of electromagnetic radiation of which visible light is only a small subset.

When distinguishing colors of light in the visible portion of the spectrum the values are typically given in nanometers. There are 10^{9} nm per meter.

**Example 2:** What color is light with a frequency of 4.29 × 10^{14} Hz?
\begin{align*}
c & = \lambda \nu \\\\
\lambda & = \frac {c}{\nu } \\\\
\lambda & = \frac {3.00 \times 10^8 \, \frac{m}{s}}{4.29 \times 10^{14} \, \frac{1}{s} } \\\\
\lambda & = 6.99 \times 10^{-7} \, m
\end{align*}
We need to convert this into nanometers to read the color off the chart.
$$ 6.99 \times 10^{-7} \, m \times \frac {10^9 \, nm}{ 1 m } = 699 \, nm $$
We can now see that this radiation is red light since it is between 620 nm and 750 nm.