Download This is a highly abstract subject

Atomic Structure
This is a highly abstract subject. To make learning easier, try to imagine atoms and electrons as everyday objects. There
are several types of facts which you will need to know to successfully complete the quiz on this subject:
History of atomic structure discoveries. These discoveries have shaped the direction of all the natural sciences and
thus are extremely important.
In order to understand all the discoveries in the structure of atoms, it is necessary to understand the behavior of
electromagnetic radiation.
Allowable values for quantum numbers. These are usefully viewed as descriptions of “locations” of electrons with
respect to a nucleus.
Order of orbital energy levels. Allows us to predict the behavior of any element based on the orbitals in which its
valence electrons reside.
History of Atomic Structure Discovery
1. Sir William Crooke’s (1879) calls the negatively charged “rays” produced in vacuum tubes cathode rays. These
cathode ray tubes are used by Joseph Thompson (1897) to determine the charge to mass (or mass to charge) ratio of the
electron. The mass to charge ratio of these cathode rays (electrons) does not depend on the gas in the cathode ray tube or
on the metal from which the cathode or anode are constructed.
2. [Not in our text, but an important discovery] Canal rays (positive particles) are discovered (1886) in modified cathode
ray tubes. The charge to mass ratio of numerous canal rays are measured later and these ratios do depend on the type of
gas in the cathode ray tube. The lightest of these particles are produced when the gas is hydrogen and the canal rays
produced are called protons.
3. Millikan’s (1909) oil drop experiment is used to determine the charge of the electron. This is combined with the mass
to charge ratio to determine the mass of the electron (0.000548 amu).
4. Three types of radioactivity are discovered (α, β, and γ) and used to investigate the structure of the atom.
5. Rutherford uses α particles to determine that the protons present in the atoms are located in a small volume called the
nucleus. By this time the charge of the proton had been determined to be of equal magnitude, but of opposite sign of the
charge of the electron and the mass of the proton was determined to be 1.0073 amu.
6. Chadwick (1932) discovers the neutron by bombarding Be foil with α particles. It is also determined that neutrons are
appear to be “made up of” one proton and one electron. The mass of the neutron is 1.0087 amu. Note that the mass of the
electron + the mass of the proton ≠ the mass of the neutron. This apparent inconsistency with the law of conservation of
mass is explained by Einstein’s famous equation, E = mc2. We will learn more about this later in this academic year.
All these discoveries led to a new model of the atom. This model had the massive particles in the nucleus of the atom
which was 0.0001 times smaller than the size of the atom. These facts do not address what the electrons do in atoms.
This has to be understood in “light” of discoveries made about atomic emission of electromagnetic radiation that were
occurring prior to and concurrently with the above discoveries.
Facts about the wave theory of light. Light is viewed as electromagnetic waves (two waves, one electric and one
magnetic, perpendicular to one another). Important features of these waves include: the wavelength, the frequency, and
the speed of light. They are related by the equation ν = c/λ (with c = 2.998 x108 m/sec).
Light is refracted by gratings or prisms and the different wavelengths of light are bent through different angles. Thus light
can be separated into its components. It is found that “white light” is made up of the whole spectrum of visible colors of
light (ROYGBIV). However, emission from gas filled tubes creates only narrow lines (not the whole spectrum).
Different lines are created when different gases are used.
In 1885 Balmer found that the frequency of the visible light emitted by hydrogen gas in an electric discharge could be
represented by an equation which he derived empirically (not based on a theory but on experimental data).
1
1
ν = Rc ( 2 )
n2
2
where R = the Rydberg constant, which has a value of 10,967,800 m-1, n is a whole number (1, 2, 3, . . . ), and c is the
speed of light. This equation does not make sense in the context of classical physics which states that the frequency of
light should exist as a continuum.
(continued)
2
In 1900 Max Planck proposed that light energy is not a continuum but discrete energy packets called quanta. The
equation relating light energy to frequency is E = hν. (h = 6.626 x 10-34 Js)
Now things are getting really interesting. In 1887 Hertz did some experiments on the interaction of light with metals.
Shining light on a metal foil can cause the build-up of positive charge. The charge only developed when the light used
had a frequency (and thus energy) greater than some threshold value. The threshold was different for different metals.
The amount of charge developed depended on the “brightness” of the light.
In 1905 Albert Einstein did some theorizing and related Planck’s results to the work done by Hertz. The equation E = hν
explains the threshold value observed in the photoelectric effect. The quanta of light would later become known as
photons.
Now we can put the pieces together.
1. Light is quantized (photons) E = hν. (h = 6.626 x 10-34 Js)
2. Light in atomic spectra is quantized (Balmer series)
3. In the photoelectric effect it was determined that light energy could be related to the energy required to remove an
electron from a metal.
4. Thus, the energy of the electrons in the atom must be quantized (in discrete packets).
The Bohr Model of the Atom is Developed (1913)
1. There is only a fixed set of allowed orbits in the H atom. As long as the electron stays in an orbit, no light is emitted.
2. e- can pass from one orbit to another. The energy difference must be quantized (E = hν).
3. The allowable orbits are determined by a property of the e- called angular momentum (momentum = mass · velocity).
This property must have values of nh/2π where n = 1, 2, 3, . . .
The size (radii) of the orbits is given by n2ao with ao = 0.53 Å.
A point revisited: Einstein proposed quanta of light were photons (particles) of light. However, most phenomena of light
can be explained by wave properties. Light would now be viewed as a particle-wave. It has wave properties, but also
behaves like a particle in the photoelectric effect. Light is a “wavicle”.
In 1924, Louis de Broglie made a startling proposition about the nature of matter. Not only does light display particle-like
characteristics, but small particles display wavelike properties when they travel at high speeds (like electrons do). The de
Broglie equation relates the mass, velocity, and wavelength of particles.
During the 1920’s Bohr and Heisenberg thought about how precisely the behavior of subatomic particles can be
determined. Two properties need to be determined: the position of the particle (x) and the momentum of the particle
(essentially the velocity of the particle, since momentum (p) = mv. The result that they arrived at (in 1928) is known as
the Heisenberg Uncertainty Principle: ∆x⋅∆p = h/4π. Thus, we cannot simultaneously know both the position and
momentum of a small particle both with high accuracy. This is because our efforts to measure one of these characteristics
will alter the system we are measuring.
This result requires questioning of Bohr’s model of the atom as it places the electron in a circular orbit around the atom.
In 1926, while visiting a ski resort, Erwin Schrödinger developed an equation to account for the wavelike properties of
electrons as proposed by de Broglie. The set of equations he developed were known as wave equations and these
equations can be used to predict the region of space in which it is probable to find the electrons (a particle but treated as a
wave) around an atom. The wave equations (wavefunctions) are given the symbol ψ. Also, ψ2 gives the probability of
locating an electron in a given region of space. These probabilities can be converted into plot of electron density. These
wavefunctions are related to a set of three quantum numbers, including the quantum number, n, from the Bohr model.
These quantum numbers: n, the principle quantum number; l, the orbital quantum number; and ml, the magnetic quantum
number describe the regions of space which may be occupied by electrons (orbitals). An additional quantum number,
electron spin (ms), is also needed to unambiguously describe each electron (since each orbital can contain two electrons).
We now have a modern model of the atom. A very small, dense, nucleus (d ~ 0.0001 to 0.0005 Å) composed of protons
and neutrons (the two “massive” subatomic particles). Surrounding the nucleus are orbitals - regions of space where the
probability of finding electrons is high (when the orbital is actually occupied).