Chapter 6: Electronic Structure of Atoms
o The distance between corresponding points on adjacent waves is the wavelength ().
o The number of waves passing a given point per unit of time is the frequency ().
o For waves traveling at the same velocity, the longer the wavelength, the smaller the
o All electromagnetic radiation travels at the same velocity: the speed of light (c),
3.00 10 m/s.
o Therefore, c =
The Nature of Energy
o Max Planck explained it by assuming that energy comes in packets called quanta.
o Einstein used this assumption to explain the photoelectric effect.
o He concluded that energy is proportional to frequency:
E = h
where h is Planck’s constant, 6.626 104J-s.
o Therefore, if one knows the wavelength of light, one can calculate the energy in one
photon, or packet, of that light:
E = h
o For atoms and molecules one does not observe a continuous spectrum, as one gets
from a white light source. Only a line spectrum of discrete wavelengths is observed.
o Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:
Electrons in an atom can only occupy certain orbits (corresponding to certain
Electrons in permitted orbits have specific, “allowed” energies; these energies
will not be radiated from the atom.
Energy is only absorbed or emitted in such a way as to move an electron from
one “allowed” energy state to another; the energy is defined by E = h
The energy absorbed or emitted from the process of electron promotion or
demotion can be calculated by the equation:
where R is the Rydberg constant, 2.18 1018J, and n and n are the
H i f
initial and final energy levels of the electron.
The Wave Nature of Matter
o Louis de Broglie posited that if light can have material properties, matter should exhibit
o He demonstrated that the relationship between mass and wavelength was
The Uncertainty Principle
o Heisenberg showed that the more precisely the momentum of a particle is known, the
less precisely is its position known:
o In many cases, our uncertainty of the whereabouts of an electron is greater than the
size of the atom itself!
o Erwin Schrödinger developed a mathematical treatment into which both the wave and
particle nature of matter could be incorporated; known as quantum mechanics.
o The wave equation is designated with a lower case Greek psi ().
o The square of the wave equation, , gives a probability density map of where an
electron has a certain statistical likelihood of being at any given instant in time.
o Solving the wave equation gives a set of wave functions, or orbitals, and their
Each orbital describes a spatial distribution of electron density.
An orbital is described by a set of three quantum numbers.
Principal Quantum Number (n)
o The principal quantum number, n, describes the energy level on which the orbital
o The values of n are integers ≥ 1.