A complete description of the nature of light requires two explanations.
All of the different behaviours of light can be explained by one (or both) of its wave and particle properties. Light waves The amplitude is the height of a wave. The wavelength is the distance between two successive crests or troughs in the wave. This can be measured in metres (m), micrometres (microns, µm =10^{6} m), nanometres (nm = 10^{9} m) or angstroms (Å = 10^{10} m). The reciprocal of wavelength is called wavenumber and is often used in spectroscopy to express a wavelength or a wavelength range. The unit for wavenumber is cm^{1} which, in effect, represents the number of waves in a cm. The frequency is the number of waves that pass by in 1 second. It has the unit Hertz (Hz). A frequency of 1 000 Hz means that 1 thousand complete wave cycles (crest to crest or trough to trough) pass by each second. The velocity (speed) of a wave can be related to its frequency (, called 'Nu') and wavelength (, called 'Lambda') by the rule:
where c = the speed of the light wave = 3 x 10^{8} ms^{1 } (in a vacuum) Given that c is constant, this equation tells us that
and
must be inversely proportional to each other. That is, as one variable
increases, the other decreases. Solution
Photons The energy of a photon is directly proportional to frequency (energy increases with increasing frequency) and is given by the rule:
Combining this rule with the rule for wave speed we obtain: As you would expect, given the relationship between and , this equation shows that energy is inversely proportional to wavelength (energy increases as wavelength decreases). Overall, the energy equations tell us that high frequency/short wavelength light has high energy and low frequency/high wavelength light has low energy. On the electromagnetic spectrum therefore, Xrays have relatively high energy and radio waves have low energy. Within the visible part of the spectrum, violet has the most energy because it is at the high frequency end and red has the least because it is at the low frequency end. Sample problem: Note that the energy of Xrays is usually expressed in electron volts (eV): 1 J = 6.24 X 10^{18} eV Therefore, the energy of the 2.6 Å Xray photon is equal to:
