**Electromagnetic Radiation** comprises the various types or forms of radiation which propagate through space that are not associated with mass.

Electromagnetic radiation behaves in most circumstances as waves [Figure 7.1 p 276] and can thus be characterized as waves.

Three parameters determine a wave:

- Frequency (
*f*or ), the rate at which wave crests pass a given point. Units = sec^{-1}(s^{-1}) or Hz (animation on**slide**) - Wavelength (
**), the distance between repeating points on a wave (crest - crest, etc.). Units = meters, nm, Å (= 10**^{-10}m) etc. - Speed (v), rate of propagation of a given point on a wave. Units = m/sec = m*s
^{-1}.

These parameters are related by the the expression:

For electromagnetic radiation (light) the speed is defined in a vacuum: v = c = 2.9979 x 10^{8}m/s

It turns out that the energy associated with light is not continuous like an ocean wave, but rather is "packaged' as we would expect with a particle, and the energy/package is proportional to the frequency. Thus the energy per packet, or **photon** is:

**E _{photon} = hf = E_{photon} = hc/**

h = Plank's constant = 6.626 x 10^{-34}J*s

Rewriting, ** h f = hc/**

Example:What is the energy of a 400.0 nm photon?

E _{photon}= hc/

E _{photon}= (6.626 x 10^{-34}J*s)(2.9979 x 10^{8}m/s) / (4.000 x 10^{-7}m) =4.966 x 10^{-19}J

As particles photons also exhibit momentum (mv), that is, in reflecting off a surface they act as if they were particles with a certain mass and velocity. Though photons themselves don't have "mass"* per se*, their energy can be interconverted to mass via Einstein's famous equation:

Example:What is the energy of 1 g of matter?

E= mc ^{2}

E = (0.001 kg)(2.9979 x 10 ^{8}m/s)^{2}

E = 9 x 10^{13}kJ(Note a Joule = kg m

^{2}s^{-2}, this corresponds to about 22 megatons of TNT, or 2,000 times more powerful than the Hiroshima atom bomb! Or, in other words, the Hiroshima bomb only converted about half a milligram of mass to energy!)

Since light has matter-like properties, perhaps matter has light-like (wave) properties. In the 1920's de Broglie noted that one could set the energy relationships above equal to each other and postulate a wavelength for matter particles:

dividing both sides by c^{2},

m = hc/c

^{2}= h/c for photons, but since matter moves at less than c,

It turns out that small particles such as electrons do indeed behave as if they are waves under certain circumstances.

As an example, for an electron with mass = 9.11 x 10^{-31}kg traveling at 4 x 10^{4}m/s:

Compare this to the wavelength of visible light (400 - 700 nm). This is why electron microscopes are so valuable - they have much greater resolution since the wavelengths are much shorter. Other particles, such as neutrons have higher masses and thus shorter wavelengths so they should have even greater potential resolution. Today folks have even created systems where atoms may be used as probes using their wave-like properties.

**Waves vs. Particles:** which is true? General discussion of particle-wave duality. (Double slit experiment - If you would like a nice low key cartoon introduction to this aspect of "quantum wierdness" try this link: http://www.youtube.com/watch?v=DfPeprQ7oGc)

Another great, and confusing, discovery of the nineteenth century was that atoms give off *line spectra* rather than continuous spectra. [Fig. 7.6, p 300]

Under classical pictures we would expect a continuous spectra. This is because electrons give off light when they are forced to change directions or slow down. Thus line spectra indicate that electrons exist in some kind of structured environment within the atom - not every speed or "orbit" can be available to them.

As you might imagine the simplest line spectra is owned by hydrogen. By the late nineteenth century folks had found that the line spectra of hydrogen could be described by a simple, empirical, mathematical relationship, known as the **Rydberg equation**:

It turns out that hydrogen's spectra consists of a repeating pattern of lines. The first set, the **Lyman series**, occurs in the ultraviolet (UV) and is described by the Rydberg equation with n_{1} = 1, the second, the **Balmer series**, occurs in the visible and is described by the Rydberg equation with n_{1} = 2,

The third set, the **Paschen series**, occurs in the infrared (IR) and is described by the Rydberg equation with n_{1} = 3.

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*© R A Paselk*

*Last modified 11 March 2015*