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Quantum Theory and Electrons 109
All electromagnetic radiation travels at about the same speed in a vacuum,
3.00 10 8 m/s. This constant, c, is the speed of light and is the product of the
frequency and the wavelength:
c
Therefore, we can represent the energy change in terms of the wavelength and
speed of light:
7-2 Bohr’s Model
E hc/
Niels Bohr developed the first modern atomic model for hydrogen using the
concepts of quantized energies—the energies associated with the atom could
only be of certain discrete values. The Bohr model postulated a ground state for
the atom, an energy state of lowest energy, and one or more excited states,
energy states of higher energy. In order for an electron in an atom to go from
its ground state to an excited state, it must absorb a certain amount of energy
and if the electron dropped back from that excited state to its ground state, it
must emit that same amount of energy. Bohr’s model also allowed the development
of a method of calculating the energy difference between any two energy
levels:
E 2.18 1018 J ¢ 1
n2
final
1
n2 ≤
initial
The constant 2.18 10 18 J is the Rydberg constant, R H. The n’s are integers
associated with the initial and final energy levels.
7-3 Quantum Mechanics
Bohr’s model worked relatively well for hydrogen, but not very well at all for
any other atom. Early in the 1900s, Schrödinger created a more detailed model
and set of equations that better described atoms by using quantum mechanical
concepts. His model introduced a mathematical description of the electron’s
motion called a wavefunction or atomic orbital. Squaring the wave function
(orbital) gives the volume of space in which the probability of finding the electron
is high, the electron cloud (electron density).