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General Chemistry Principles, Patterns, and Applications, 2011

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As you will soon see, the energy of electromagnetic radiation is directly proportional to its frequency <strong>and</strong> inversely<br />

proportional to its wavelength:<br />

Equation 6.3<br />

E µn<br />

Equation 6.4<br />

E µ1l<br />

Whereas visible light is essentially harmless to our skin, ultraviolet light, with wavelengths of ≤ 400 nm, has enough<br />

energy to cause severe damage to our skin in the form of sunburn. Because the ozone layer described in Chapter 3<br />

"Chemical Reactions"absorbs sunlight with wavelengths less than 350 nm, it protects us from the damaging effects of<br />

highly energetic ultraviolet radiation.<br />

Note the Pattern<br />

The energy of electromagnetic radiation increases with increasing frequency <strong>and</strong> decreasing wavelength.<br />

E X A M P L E 1<br />

Your favorite FM radio station, WXYZ, broadcasts at a frequency of 101.1 MHz. What is the wavelength of<br />

this radiation?<br />

Given: frequency<br />

Asked for: wavelength<br />

Strategy:<br />

Substitute the value for the speed of light in meters per second into Equation 6.2 to calculate the<br />

wavelength in meters.<br />

Solution:<br />

From Equation 6.2, we know that the product of the wavelength <strong>and</strong> the frequency is the speed of the<br />

wave, which for electromagnetic radiation is 2.998 × 10 8 m/s:<br />

λν = c = 2.998 × 10 8 m/s<br />

Thus the wavelength λ is given by<br />

l = cn = ((2.998 ´108 m / s101.1 MHz))<br />

((1 MHz106 s -1) = 2.965 m<br />

Exercise<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

502

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