SECTION 2:
QUANTUM THEORY
AND THE ATOM
CHAPTER 9: ELECTRONS IN
ATOMS AND THE PERIODIC TABLE
Learning Goals
• Compare the Bohr and quantum
mechanical models of the atom.
• Explain the impact of de Broglie’s wave
particle 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.
Bohr’s Model of the Atom
• Einstein’s theory of light’s dual nature
accounted for several unexplainable
phenomena, but it did not explain why
atomic emission spectra of elements
were discontinuous.
Bohr’s Model of the Atom
• In 1913, Niels Bohr, a Danish
physicist working in Rutherford’s
laboratory, proposed a quantum
model for the hydrogen atom that
seemed to answer this question.
•This model correctly predicted the
frequency lines in hydrogen’s atomic
emission spectrum.
Bohr’s Model of the Atom
• 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
• Bohr suggested that an electron
moves around the nucleus only in
certain allowed circular orbits.
Bohr’s Model of the Atom
• Each orbit was given a
number, called the
quantum number.
•Bohr orbits are like steps of
a ladder, each at a specific
distance from the nucleus
and each at a specific
energy.
Bohr’s Model of the Atom
• Hydrogen’s single electron is in the n = 1
orbit when it is in the ground state.
•When energy is added, the electron moves
to the n = 2 orbit.
Bohr’s Model of the Atom
• The electron releases energy as it
falls back towards the ground state.
Bohr’s Model of the Atom
• Bohr’s model explained the
hydrogen’s spectral lines, but failed
to explain any other element’s lines.
• For this and other reasons, the Bohr
model was replaced with a more
sophisticated model called the
quantum-mechanical or wavemechanical model.
Quantum Mechanical Model
• Louis de Broglie (1892–1987)
hypothesized that particles, including
electrons, could also have wavelike
behaviors.
•Electrons do not behave like particles
flying through space.
• We cannot, in general, describe their
exact paths.
Quantum Mechanical Model
• Heisenberg showed it is impossible to
take any measurement of an object
without disturbing it.
• 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.
Quantum Mechanical Model
• The only quantity that can be known
is the probability for an electron to
occupy a certain region around the
nucleus.
Quantum Mechanical Model
• Schrödinger treated electrons as
waves in a model called the
quantum mechanical model of the
atom.
•Schrödinger’s equation applied equally
well to elements other than hydrogen
(unlike Bohr’s model).
Quantum Mechanical Model
• The quantum mechanical model
makes no attempt to predict the path
of an electron around the nucleus.
•Bohr orbits were replaced with
quantum-mechanical orbitals.
Quantum Mechanical Model
• Orbitals are different from orbits in that
they represent probability maps that
show a statistical distribution of where
the electron is likely to be found.
Quantum Mechanical Model
• In the quantum-mechanical model, a
number and a letter specify an
orbital.
•The lowest-energy orbital is called the
1s orbital.
• It is specified by the number 1 and the
letter s.
Hydrogen’s Atomic Orbitals
• The number is called the Principal
quantum number (n) and it
indicates the relative size and
energy of atomic orbitals.
•n specifies the atom’s major energy
levels, called the principal energy
levels.
Hydrogen’s Atomic Orbitals
• Energy sublevels are contained
within the principal energy levels.
Hydrogen’s Atomic Orbitals
• Each energy sublevel relates to
orbitals of different shape.
s, p, d, f
s, p, d
s, p
s
Hydrogen’s Atomic Orbitals
• s sublevel:
Hydrogen’s Atomic Orbitals
• p sublevel:
Hydrogen’s Atomic Orbitals
• d sublevel:
Hydrogen’s Atomic Orbitals
• f sublevel:
Hydrogen’s Atomic Orbitals
• Orbitals are sometimes represented by
dots, where the dot density is proportional
to the probability of finding the electron.
• The dot density for the 1s orbital is
greatest near the nucleus and decreases
farther away from the nucleus.
• The electron is more likely to be found
close to the nucleus than far away from it.
Hydrogen’s Atomic Orbitals
Hydrogen’s Atomic Orbitals
• At any given time, hydrogen’s
electron can occupy just one orbital.
•When hydrogen is in the ground state,
the electron occupies the 1s orbital.
•When the atom gains a quantum of
energy, the electron is excited to one of
the unoccupied orbitals.