Chapter 7
Quantum Theory & Electronic Structure of the Atom
 electronic structure : the arrangement of electrons in an atom
Observations leading to our Understanding of Electronic Structure
Much of our understanding of electronic structure evolved from analysis of light emitted or absorbed by
substances. Visible light is a form of electromagnetic radiation (aka radiant energy). All forms of
electromagnetic radiation travel through a vacuum at 3.00 H 108 m·s−1 (“the speed of light”).
Electromagnetic radiation shows properties that indicate it travels in waves.
 wavelength, λ: distance per wave cycle
 frequency, ν: number of wave cycles per unit time
 amplitude: height of wave crests from baseline
distance cycles distance
×
=
cycle
time
time
λν = c = 3.00 H 108 m·s−1
Electromagnetic Spectrum Fig. 7.3
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Eqn. 7.1
SI Unit of Frequency
 Hertz, Hz = s–1 or 1/s.
1 kHz = 1000 Hz = 1000 cycles/second
1 MHz = 106 Hz = 106 cycles/second
Example: A sodium vapor streetlight emits light with a wavelength of 589 nm. What is the frequency of the
radiation?
Atomic Line Spectra: light
emitted by electrically excited
gaseous atoms does not contain
all the wavelengths/frequencies
of natural light (a continuous
spectrum). Only certain colors
of light are emitted!
This line spectrum can be
used to identify the element!
In 1885, Balmer discovered a
relationship for the frequencies
of the 4 lines in hydrogen’s
visible line spectrum:
 R  1 1 
ν = H  2  2 
 h  2 n 
where RH = 2.18 H 10–18 J,
h = 6.63 × 10–34 J·s,
and n = 3, 4, 5, or 6.
 Figure 7.7
Bohr Model of the Atom
Soon after the nuclear model of the atom was proposed (Rutheford’s gold foil experiment), Neils Bohr
proposed a model for the electronic structure of the atom based on the observations above.
In this model, electrons orbit the nucleus in certain allowable energy levels and do not emit any energy as
long as they stay in the same energy level.
When an electron moves from one energy level to another, a photon is absorbed or emitted whose energy
equals the difference in energy between the two states.
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Mathematically, the allowed energy levels for an electron in the
hydrogen atom can be calculated:
 1 
En =  R H  2 
n 
The zero-point energy is when the electron is completely removed
from the atom (i.e., n=∞). Thus the energies of all the other levels
are negative.
When an electron is in the lowest energy state possible, we say it is
in a ground state. When an electron is in a higher energy state, we
say it is in an excited state.
Analogy for atomic energy levels
When an electron moves from an orbit of higher energy to one of lower energy,
the atom EMITS energy in the form of a photon.
When an electron moves from an orbit of lower energy to one of higher energy,
the atom ABSORBS energy from a photon.
For a one-electron system with a nucleus of an atom other than hydrogen, we can adjust the energy equation
above by inserting the square of the atomic number (Z 2) as a factor before RH.
The Bohr model of the atom could only describe one-electron systems (i.e., H, He+, Li2+, etc.) accurately. We
need a new model to be able to describe multi-electron atoms!
Quantum-Mechanical (QM) Model
1926: Erwin Schrödinger proposes wave functions to describe the motion of electrons.
, = E
where , is the “Hamiltonian operator”, a set of mathematical functions,
E is the energy of the atom, and
 is the wave function.
2
  expresses the probability that an electron is at a certain location in the atom at a certain time.
 The solutions to the wave functions are called orbitals.
(No relation to “electron orbits” of Bohr’s model!)
A-B. Electron probability density in ground-state H atom
C-D. Total probability of finding electron within a spherical layer
E. Representation of the layer with the largest probability
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