• Review of 5.1:
• All waves have distinct amplitudes,
frequency, periods and wavelengths.
• All electromagnetic waves travel at the
speed of light. C = (3.0x108 m/s)
• C = f
• The relationship between the energy
and frequency is E = hf
• All elements have their own individual
atomic emission spectrum and
absorption spectrum.
Section 5.2 Quantum Theory and the Atom
• Compare the Bohr and quantum mechanical models
of the atom.
• Explain the impact of de Broglie's wave article duality
and the Heisenberg uncertainty principle on the
current view of electrons in atoms.
• Identify the relationships among a hydrogen atom's
energy levels, sublevels, and atomic orbitals.
atom: the smallest particle of an element that retains
all the properties of that element, is composed of
electrons, protons, and neutrons.
Section 5.2 Quantum Theory and the Atom (cont.)
ground state
quantum number
de Broglie equation
Heisenberg uncertainty
principle
quantum mechanical model
of the atom
atomic orbital
principal quantum number
principal energy level
energy sublevel
Wavelike properties of electrons help
relate atomic emission spectra, energy
states of atoms, and atomic orbitals.
Bohr's Model of the Atom
• The dual wave-particle model of light could
not explain all phenomena of light. In
particular, it couldn’t explain why emission
spectra was discontinuous.
• Niels Bohr, a Danish physicist that worked
in Rutherford’s lab, proposed a model that
would match hydrogen’s emission
spectrum.
• In Bohr’s model, the atom has only certain
allowable energy states. (circular orbits)
• The lowest allowable energy state of an
atom is called its ground state.
• When an atom gains energy, it is in an
excited state.
Bohr's Model of the Atom (cont.)
• In Bohr’s model, atom’s with smaller energy states will
have electrons in smaller orbits.
• Even Hydrogen can have many different excited states,
depending on where its one electron is located.
Bohr's Model of the Atom (cont.)
• Each orbit was given a number, n, called
the quantum number.
Bohr's Model of the Atom (cont.)
• Hydrogen’s single electron is in the n = 1
orbit in the ground state. No energy
radiates in this state.
• When energy is added, the electron moves to
the n = 2 orbit. This raises the electron to an
excited state.
• If the electron would then drop from the
higher orbit to a lower one, it will release
energy in the form of a photon as it drops.
The photon corresponds to the energy
difference between the two levels.
• (p.148)
• Because there are only certain energy
levels, there are only certain frequencies
of radiation that can be emitted. E = hf
• Think of this like rungs of a ladder.
• Just as you can only go up or down from
rung to rung, an electron can only move
from one orbit to another.
• Unlike ladder rungs, however, the energy
levels are not evenly spaced.
• Electrons that drop from higher-energy
orbits down to the 2nd orbit make all
hydrogen’s visible lines—the Balmer series.
• Electrons in Hydrogen that drop from higher
levels to the 1st orbit release ultraviolet light
and are in the Lyman series.
• Electrons in Hydrogen that drop from higher
orbits to the 3rd orbit radiate infrared and are
in the Paschen series.
Bohr's Model of the Atom (cont.)
Bohr's Model of the Atom (cont.)
Bohr's Model of the Atom (cont.)
• Bohr’s model explained the hydrogen’s
spectral lines, but failed to explain any
other element’s lines.
• The behavior of electrons is still not fully
understood, but it is known they do not move
around the nucleus in circular orbits.
The Quantum Mechanical Model of the Atom
• Mid 1920s, Frenchman Louis de Broglie
(1892–1987) hypothesized that particles,
including electrons, could also have
wavelike behaviors.
• He compared light waves to waves made
on musical instruments with fixed ends.
• On the instruments, only multiples of half
wavelengths are possible.
• Similarly, de Broglie reasoned that only odd
numbers of wavelengths are allowed in a
circular orbit with a fixed radius.
The Quantum Mechanical Model of the Atom
(cont.)
• The figure illustrates that electrons orbit the
nucleus only in whole-number wavelengths.
The Quantum Mechanical Model of the Atom
(cont.)
*de Broglie proposed that if waves can act
like particles, the reverse must also be
true.
The de Broglie equation predicts that all
moving particles have wave characteristics.
 represents wavelengths
h is Planck's constant.
m represents mass of the particle.
 represents velocity .
• If all moving particles generate waves, why don’t we see
them? Let’s look at a car moving at 25 m/s and having a
mass of 910-kg. What wavelength of light will it have?
• German Werner Heisenberg (1901-1976), showed it is
impossible to take any measurement of an object without
disturbing it.
• Heisenberg compared trying to measure an electron’s
position to trying to find a helium-filled balloon in a
darkened room.
• The Heisenberg uncertainty principle
states that it is fundamentally impossible to
know precisely both the velocity and position
of a particle at the same time.
• The only quantity that can be known is the
probability for an electron to occupy a certain
region around the nucleus.
The Quantum Mechanical Model of the Atom
• (cont.)
When a photon interacts with an electron at rest,
both the velocity and position of the electron are
modified.
• The Heisenberg uncertainty principle states that
it is fundamentally impossible to know precisely
both the velocity and position of a particle at the
same time.
The Quantum Mechanical Model of the Atom
(cont.)
• 1926, Austrian Erwin Schrodinger (1887-1961)
continued the wave- particle theory.
• Schrödinger treated electrons as waves in a model
called the quantum mechanical model of the
atom.
• Like Bohr’s model, this model limits an electron’s
energy to certain values. It does not try to
describe the electron’s path. His model is a very
complex model using wave functions.
• Schrödinger’s equation applied equally well to
elements other than hydrogen.
The Quantum Mechanical Model of the Atom
(cont.)
• The wave function predicts a three-dimensional
region around the nucleus called the atomic
orbital.
• The density at a given point is proportional to the
probability of finding an electron at that point.
Hydrogen Atomic Orbitals
• Just as Bohr’s model had numbers assigned to
electron orbits, so does the quantum mechanical
model. There are 4 quantum numbers for
orbitals.
• Principal quantum number (n) indicates the
relative size and energy of atomic orbitals.
• n specifies the atom’s major energy levels, called the
principal energy levels. As n increases, the orbital
is larger and the atom’s energy increases. The
lowest principle energy level has a principal quantum
number of 1.
• A hydrogen atom in ground state will have a single
electron in the n = 1 orbital.
Hydrogen Atomic Orbitals (cont.)
• Energy sublevels are contained within the
principal energy levels.
• The numbers of sublevels in a principal energy level
increase as n increase, much like there are more seats
per row as you go higher up in a stadium.
• Shapes of orbitals:
– All s orbitals are spherical
– All p orbitals are dumbbell-shaped
– d and f orbitals do not all have the same
shape.
– Orbitals in higher sublevels are bigger than
ones in lower sublevels.
– (2s is bigger than 1s)
Hydrogen Atomic Orbitals (cont.)
• Each energy sublevel relates to orbitals of
different shape.
Hydrogen Atomic Orbitals (cont.)
2
• The number of orbitals related to each sublevel
is always an odd number.
• The maximum number of orbitals for each
principal energy level equals n2.
Section 5.2 Assessment
Which atomic suborbitals have a
“dumbbell” shape?
A. s
B. f
D
A
0%
C
D. d
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. p
Section 5.2 Assessment
Who proposed that particles could also
exhibit wavelike behaviors?
A. Bohr
B. Einstein
D
A
0%
C
D. de Broglie
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. Rutherford