# Quantum Reality

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:

Ephoton = hf = hc/

where E is the energy per photon in J when is expressed in meters and

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

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

Ephoton= hc/

Ephoton= (6.626 x 10-34J*s)(2.9979 x 108m/s) / (4.000 x 10-7m) = 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:

E= mc2

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

E= mc2

E = (0.001 kg)(2.9979 x 108m/s)2

E = 9 x 1013kJ

(Note a Joule = kg m2s-2, this corresponds to about 22 megatons of TNT, or 2,000 times more powerful than the Hiroshima atom bomb!)

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:

E= mc2= hc/

dividing both sides by c2,

m = hc/c2 = h/c for photons, but since matter moves at less than c,

m = h/v, and

= h/mv

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 10-31kg traveling at 4 x 104m/s:

= h/mv

= (6.626 x 10-34J*s) / (9.11 x 10-31kg)(4 x 104m/s)

= (6.626 x 10-34kg m2s-2*s) / (9.11 x 10-31kg)(4 x 104m/s)

= 1.8 x 10-8m = 2 x 10-8m = 2 x 10 nm = 0.002 m

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 ierdness" try this link: http://www.youtube.com/watch?v=DfPeprQ7oGc)

# Quantum Models of the Atom

When we introduced atoms earlier (Lecture 4) we left off with Rutherford's discovery that atoms must be mostly empty space, with a tiny, massive, positively charged nucleus in the center and electrons circulating around it in some fashion. A tremendous problem with this picture is that an electron going in a circle (or other non-linear path) will give off light (energy) of an energy depending on its velocity and the radius of curvature. Notice that as energy is released the electron will go to a smaller orbit, give off more light etc. Under the classical picture an atom should collapse with a flash of light nearly instantaneously. We're still here, so there's a problem!

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:

where R = the Rydberg constant, NOT the Gas constant.

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 n1 = 1, the second, the Balmer series, occurs in the visible and is described by the Rydberg equation with n1 = 2,

The third set, the Paschen series, occurs in the infrared (IR) and is described by the Rydberg equation with n1 = 3.

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