Chem 109 - General Chemistry - Spring 2015

Lecture Notes 21: 11 March

Atomic Structure & Electromagnetic Radiation (Light), cont.

diagram of electromagnetic spectrum

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.

Labeled sine wave diagram

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^-10m) 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:

v = f•

For electromagnetic radiation (light) the speed is defined in a vacuum: v = c = 2.9979 x 10⁸m/s

c = f• in vacuo

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:

E_photon = hf = E_photon = 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

Rewriting, hf = hc/

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

E_photon= hc/

E_photon= (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! 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:

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

Atomic Structure & Chemical Periodicity

Quantum Models of the Atom

When we introduced atoms earlier (Lecture 5) 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]

image of spectrum of star K4iii

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, and n is an integer with n₂> n₁.

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,

image of hydrogen line spectrum