PhysicsLAB Resource Lesson
Atomic Models and Spectra

Printer Friendly Version
The first atomic theory of matter was developed as early as 500 BC by Democritus, in which he believed that matter was made up of particles so small that they could not be further subdivided. He further postulated that different substances has different properties because of the differences in the nature of their "atoms." However, his theories were not supported by Aristotle, 300 BC, who thought that matter was continuous, not discrete. He advocated that every object on the earth was made up of some combination of only four substances:  earth, water, fire, and air. It took over 2000 years for Aristotle's philosophy to be replaced by the concept that matter was not just composed of only those four general substances to its being comprised of unique elements - hydrogen, carbon, oxygen, sulfur, etc. These elements combined chemically in specific ratios and followed patterns which Mendeleev arranged and predicted in his periodic table. Arguments existed over whether or not there was a smallest representative of an element, an "atom." Einstein's explanation of "Brownian motion (1905)" along with a huge compilation of other experimental data, lead physicists to believe that "atoms" were about 10-10 meters in diameter and were electrically neutral. But want did an "atom" really looked like?
 
One of the first atomic models was that proposed by J.J. Thomson after he discovered the existence of the electron as a result of his work with cathode rays. Since each atom was electrically neutral, Thomson thought that it consisted of a relatively large, uniformly distributed, positive mass with negatively charged electrons  embedded in it like "raisins in a plum pudding."
 
 
Rutherford’s gold-foil experiment.
 
It was Thomson's model that Rutherford, Geiger, and Marsden were testing with their historical gold-foil experiment (1909).
 
 
Rutherford’s plan was to aim alpha particles, the nucleus of helium nuclei, at a thin gold foil and observe the scattering pattern on a zinc sulfide screen which would show small bursts of light when struck by an alpha particle. Although the majority of the alpha particles passed through undeflected, some were strongly deflected into hyperbolic paths while others were scattered through almost 180°. These dramatically recoiled alpha particles led Rutherford to use the analogy of firing bullets at a piece of tissue paper and discovering that some of the bullets bounced back!
 
 What two conclusions did Rutherford draw from these results?

 
Calculate the distance of an alpha particle’s closest approach to a gold nucleus.
 

 
Emission Spectral Lines
 
While Rutherford was doing his pioneering work leading to the discovery of the atomic nucleus, chemists were completing spectra analysis of different elements. They found that each element, when excited in its gaseous state, produced a unique spectral fingerprint of brightly colored lines which could be seen when viewed through closely separated slits. The element most studied was hydrogen which had three distinctively observable lines in the visible spectrum - red, blue/cyan, and violet. It was noted that the lines were always there and that the spacing between these lines became smaller and smaller.
 
 
The first person to propose a mathematical relationship for these lines was J. J. Balmer and we now call hydrogen's visible spectrum the Balmer series. Another pattern in hydrogen's spectral lines was noted by J. Rydberg and W. Ritz. When you added together the frequencies of any two lines, you produced the frequency of a third line. There had to be an atomic model that would predict these patterns. That model was conceived by Neils Bohr (1913).
 
 
What problems did Rutherford's nuclear model encounter?
 
[1] According to classical physicists, an orbiting electron should radiate energy at a frequency that would match its orbital frequency. Eventually, it would radiate its energy completely away, moving closer and closer to the nucleus with each rotation. Emitting a continuous spectrum of electromagnetic radiation as it spiraled to its demise. This would result in the collapse of matter, and chemistry, as we know it.
 
[2] Atoms in a gaseous state produced unique, discrete line spectra, not continuous spectra.
 
 
What approach did Bohr use in constructing his model of the hydrogen atom in 1913?
 
ENERGY. Bohr combined Einstein’s photons that were used to explain the photoelectric effect (1905) and Balmer’s empirical formula (1885) which successfully calculated hydrogen’s visible spectral lines to produce a revolutionary quantum theory.
 
Bohr's hypotheses in developing his theory of the hydrogen atom were
 
[1] The hydrogen atom can exist, without radiating any energy, in several stable, stationary, states.
 
[2] Radiation is only absorbed or released when the atom changes from one of its stationary states to another. The energy of the emitted or absorbed photon, a packet of radiant energy, is equal to the difference in the energy between these two states. This energy is emitted only by electrons during de-excitation and is quantized (While investigating blackbody radiation, Max Planck had discovered that electromagnetic energy was quantized according to the formula E = hf where h = 6.63 x 10-34 J sec and f represents the electromagnetic wave's frequency calculated according to the formula f = c/λ. He was awarded the 1918 Nobel Prize in Physics for his work on energy quanta.).
 
hf = Ef - Eo
 
[3] The quantized electron energy states correspond to electron orbitals of specific radii. This is equivalent to stating that the electron’s angular momentum is quantized.
 
 
This assumption that angular momentum is quantized was later proved to be correct based on the wavelength of the orbiting electron’s deBroglie's standing wave. It was found that an orbital radius would be stable if an integer multiple of the electron's deBroglie wavelength, ldeB = h / (mv), equaled the orbital’s circumference.
 
 
Upon cross-multiplying and rearranging, this formula matches the required relationship for the assumption of the electron’s quantized angular momentum.
 
 
As stated earlier, when Planck's quantized energy is applied to Bohr's model, the energy of an emitted photon equals the difference between the energies for each accepted electron orbital, where electrons in higher orbitals have greater energies than those in lower orbitals. This explains why atomic spectra of excited gases produce discreet lines - the electrons make transitions between distinct, well-defined energy levels and lose distinct, well-defined amounts of energy during their "jumps." If you examine the diagram shown below, the highest energy photon will be blue since it is released when the electron transitions between the 4th excited state and the 1st excited state. Red is the lowest energy photon since it represents a transition only between the 2nd excited state and the 1st excited state.
 
 
These lines are in hydrogen's visible, or Balmer spectrum.
 

When electron transitions end on the ground state orbital, they produce spectral lines in the Lyman Series. This series is found in the ultraviolet portion of the electromagnetic spectrum. These photons have higher energies than any of the visible photons since ultraviolet radiation has a higher frequency. These photons are also produced when the electrons fall to a lower energy level thus releasing more energetic radiation. When electron transitions end on the second excited state's orbital, they produce spectral lines in the Paschen Series. This series is found in the infrared portion of the electromagnetic spectrum. These photons have lower energies than any of the visible photons since infrared radiation has a lower frequency. These photons are also produced when the electrons fall to a higher energy level thus releasing less energetic radiation. See the energy level diagram shown below.
 
 
 
 When does an electron absorb a photon? emit a photon?

 
When are spectra continuous instead of discrete?
 
Incandescent, high temperature, solids emit continuous spectra since electrons can fall into neighboring atoms during de-excitation and emit all possible frequencies. Excited gases emit discrete spectra which can be used to identify one gas from another since electrons must remain within ONE ATOM when undergoing energy transitions in gases.
 
As the peak frequency, fo, shifts to the right, from red to green to blue, the temperature of an incandescent solid increases. The left radiation curve would indicate a "red hot" object. The middle curve would represent a "white hot" object. And the last curve, would represent a "blue hot" object. Therefore, a red hot flame is cooler than a blue flame which is why your chemistry teacher always told you to use the "blue" portion of the bunsen burner's flame to heat your test-tubes. Red hot stars are cooler than yellow stars (our sun) which are cooler than blue stars. There are no green stars since equal amounts of longer red wavelengths and shorter blue/violet wavelengths are also emitted, producing the color white, not green.
 
 
 
What produces an absorption spectra?
 
An absorption spectra is formed when the continuous spectra emitted from an incandescent solid passes through a cool gas. The electrons in the gas absorb the exact frequencies that when excited they re-emitted. These vacancies show up as "black lines" in the solid’s spectrum.
 
These Fraunhofer lines are used by astronomers to determine which gases are present in the atmosphere of distant stars. In particular, the element helium was first discovered through an analysis of the Sun's Fraunhofer lines. Helios is the Greek name for the Sun.
 
Absorption lines are the reverse of the emission lines. That is, emission lines are bright images against a dark background. Absorption spectra consist of dark lines deleted from a contiguous "rainbow" spectrum.
 
 
An energy diagram showing absorption spectral lines show that electrons in unexcited hydrogen ABSORB exactly the same distinct wavelengths they emit when they later go through de-excitation.
 
 

 



 
Related Documents





PhysicsLAB
Copyright © 1997-2014
Catharine H. Colwell
All rights reserved.
Application Programmer
    Mark Acton