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The Quantum Model of the Atom
Electrons as Waves
The investigations into the photoelectric effect and hydrogen’s line-emission spectrum revealed that light could behave as
both a wave and a particle
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He suggested that electrons be considered waves confined to the
space around an atomic nucleus
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According
to the relationship E=hv, these frequencies corresponded to specific energies—the quantized energies of Bohr’s orbits
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Investigators demonstrated that electrons, like light waves, can be bent, or diffracted
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These experiments and other investigations also
showed that electron beams, like waves, can interfere with each other
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The Heisenberg Uncertainty Principle
In 1927, Werner Heisenberg’s idea involved the detection of electrons
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Because photons have about the same energy as electrons, any attempt to locate a specific electron with a
photon knocks the electron off its course
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The Heisenberg uncertainty principle states that tit is impossible to determine simultaneously both
the position and velocity of an electron or any other particle
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Quantization of electron energies was a natural outcome of SchrÖdinger’s
equation
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Together with
the Heisenberg uncertainty principle, the SchrÖdinger wave equation laid the foundation for modern quantum theory
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Solutions to the wave equation are known as wave functions
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Electrons exist in certain
regions called orbitals
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Atomic Orbitals and Quantum Numbers
In order to completely describe orbitals, scientists use quantum numbers
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The first three quantum numbers result from solutions
to the SchrÖdinger equation
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The fourth, the spin quantum number
describes a fundamental state of the electron that occupies the orbital
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Values of n are positive integers

The main energy levels of an atom are
represented by the principal number, n
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As n increases, the electron’s energy and its average distance from the nucleus increase
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More than one electron can have the same n value
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The total number of orbitals that exist in a given shell, or main energy level, is equal t
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The total number of orbitals that exist in a given shell, or main energy level, is equal
to nt
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The
angular momentum quantum number, symbolized by 1, indicates the shape of the orbital
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The values of l allowed are zero and all positive integers less
than or equal to n-1
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In the first energy level, n=1, there is only one sublevel possible—an s orbital
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The third energy level, n=3, has three sublevels—the s, p, and d
orbitals
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In an nth main energy level, there
are n sublevels
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For example,
the 1s sublevel is the s orbital in the first main energy level
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Magnetic Quantum Number
Atomic orbitals can have the same shape but different orientations around the nucleus
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Values of m are whole numbers, including
zero, from -1 to +1
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This orientation corresponds to a magnetic quantum number of m = 0
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The lobes of a p orbital can extend along the x, y, or z axis of a three-dimensional coordinate system
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The three p orbitals
occupy different regions of space and are related to values of m = - , m = 0, and m= +1
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The five different orientations, including one with a different shape, correspond to values of m = -2, m
= -1, m = 0, m = +1, m = +2
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The total number of orbitals at a main energy level increases with the value o n
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The orbitals s, p, and d have different shapes
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The subscripts x, y, and z indicate the three different orientations of p orbitals
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The five different
orientations of the d orbitals
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The fifth has a different
shape and a different orientation than the others
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Spin Quantum Number
An electron in an orbital behaves in some ways like Earth spinning on an axis
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To account for the magnetic properties of the electron, theoreticians of the
early twentieth century created the spin quantum number
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A single orbital can hold a
maximum of two electrons, which must have opposite spin states

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