Example 29.3 from College Physics, 29.3 Photon Energies and the Electromagnetic Spectrum

Photon Energy and Effects for UV

Short-wavelength UV is sometimes called vacuum UV, because it is strongly absorbed by air and must be studied in a vacuum. Calculate the photon energy in eV for 100-nm vacuum UV, and estimate the number of molecules it could ionize or break apart.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Using the equation $E = hf$ and appropriate constants, we can find the photon energy and compare it with energy information in Table 29.1.
Solution
The energy of a photon is given by

$E = hf = \frac{hc}{λ} .$
29.17

Using $hc = 1240 eV \cdot nm,$ we find that
$E = \frac{hc}{λ} = \frac{1240 eV \cdot nm}{100 nm} = 12 . 4 eV .$
29.18
Discussion
According to Table 29.1, this photon energy might be able to ionize an atom or molecule, and it is about what is needed to break up a tightly bound molecule, since they are bound by approximately 10 eV. This photon energy could destroy about a dozen weakly bound molecules. Because of its high photon energy, UV disrupts atoms and molecules it interacts with. One good consequence is that all but the longest-wavelength UV is strongly absorbed and is easily blocked by sunglasses. In fact, most of the Sun’s UV is absorbed by a thin layer of ozone in the upper atmosphere, protecting sensitive organisms on Earth. Damage to our ozone layer by the addition of such chemicals as CFC’s has reduced this protection for us.

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