Chapter 11
Modern Atomic Theory
Rutherford’s Atom
• The concept of a nuclear atom (charged
electrons moving around the nucleus)
resulted from Ernest Rutherford’s
experiments.
• Question left unanswered: how are electrons
arranged and how do they move?
Rutherford’s Atom (cont.)
Electromagnetic Radiation
Electromagnetic Radiation (cont.)
• Electromagnetic radiation is given off by
atoms when they have been excited by any
form of energy, as shown in flame tests.
Electromagnetic Radiation (cont.)
Figure 11.2: A seagull floating on the ocean
moves up and down as waves pass.
Electromagnetic Waves
• Velocity = c = speed of light
– 2.997925 x 108 m/s
– All types of light energy travel at the same speed.
• Amplitude = A = measure of the intensity of the
wave, i.e.“brightness”
Figure 11.3: The wavelength of a
wave is the distance between peaks.
Properties of Waves
Wavelength (λ) is the distance between identical points on successive waves.
Amplitude is the vertical distance from the midline of a wave to the peak or
trough.
7.1
Electromagnetic Waves (cont.)
• Wavelength = λ = distance between two
consecutive peaks or troughs in a wave
– Generally measured in nanometers (1 nm = 10-9 m)
– Same distance for troughs
• Frequency = ν = the number of waves that pass
a point in space in one second
– Generally measured in Hertz (Hz),
– 1 Hz = 1 wave/sec = 1 sec-1
• c=λ xν
The back and front of
a bridgerigar parrot.
University of Glasgow
The same bridgerigar parrot
seen under ultraviolet light.
University of Glasgow
Types of Electromagnetic Radiation
Planck’s Revelation
• Showed that for certain applications light energy
could be thought of as particles or photons
Planck’s Revelation
(cont.)
• The energy of the photon is directly proportional
to the frequency of light.
Mystery #1, “Black Body Problem”
Solved by Planck in 1900
Energy (light) is emitted or
absorbed in discrete units
(quantum).
E= hxν
Planck’s constant (h)
h = 6.63 x 10-34 J•s
Mystery #2, “Photoelectric Effect”
Solved by Einstein in 1905
Light has both:
1. wave nature
2. particle nature
hν
KE e-
Photon is a “particle” of light
hν = KE + BE
KE = hν - BE
7.2
Figure 11.7: Certain gases in the earth’s atmosphere
reflect back some of the infrared (heat) radiation produced by
the earth. This keeps the earth warmer than it would be otherwise.
When salts containing Li+, Cu2+, and Na+
dissolved in methyl alcohol are set on fire, brilliant colors result:
Li+, red; Cu2+, green; and Na+, yellow.
Hmco Photo Files
Problems with Rutherford’s
Nuclear Model of the Atom
• Electrons are moving charged particles.
• Moving charged particles give off energy;
therefore the atom should constantly be giving
off energy.
• The electrons should crash into the nucleus,
and the atom should collapse!!
Emission of Energy by
Atoms/Atomic Spectra
• Atoms that have gained extra energy release that
energy in the form of light.
Atomic Spectra
• Line spectrum: very specific wavelengths
of light that atoms give off or gain
• Each element has its own line spectrum,
which can be used to identify that element.
Atomic Spectra
(cont.)
Atomic Spectra
(cont.)
Figure 11.9: A sample of H atoms receives
energy from an external source and becomes
excited, then releases the energy by emitting photons.
Line Emission Spectrum of Hydrogen Atoms
An atom can release energy by emitting a photon. A particular color (wavelength) of
light carries a particular amount of energy per photon.
An atom can release energy by emitting a photon. A particular color (wavelength) of
light carries a particular amount of energy per photon.
Figure 11.10: When an excited H atom returns to a lower energy
level, it emits a photon that contains the energy released by the atom.
Figure 11.11: The colors and wavelengths
(in nanometers) of the photons in the visible
region that are emitted by excited hydrogen atoms.
Figure 11.12: Hydrogen atoms have
several excited-state energy levels.
Atomic Spectra
(cont.)
• The line spectrum must be related to energy
transitions in the atom
Figure 11.14: (a) Continuous energy levels.
Any energy value is allowed. (b) Discrete (quantized)
energy levels. Only certain energy states are allowed.
Atomic Spectra
(cont.)
• The atom is quantized, i.e. only certain energies
are allowed.
Bohr’s Model of
the Atom (1913)
1.
e- can only have specific
(quantized) energy values
2.
light is emitted as e- moves from
one energy level to a lower
energy level
En = -RH (
1
n2
)
n (principal quantum number) = 1,2,3,…
RH (Rydberg constant) = 2.18 x 10-18J
Bohr’s Model
• Explained spectrum of hydrogen
• Energy of atom is related to the distance of
electron from the nucleus
Figure 11.17: The Bohr model
of the hydrogen atom represented the electron
as restricted to certain circular orbits around the nucleus.
Bohr’s Model (cont.)
• Energy of the atom is quantized
– Atom can only have certain specific energy
states called quantum levels or energy levels.
– When atom gains energy, electron “moves” to a
higher quantum level
– When atom loses energy, electron “moves” to a
lower energy level
– Lines in spectrum correspond to the
difference in energy between levels
Bohr’s Model (cont.)
• Ground state: minimum
energy of an atom
– Therefore electrons do
not crash into the
nucleus
• The ground state of
hydrogen corresponds to
having its one electron in
the n=1 level
• Excited states: energy
levels higher than the
ground state
Bohr’s Model (cont.)
• Distances between energy levels decrease as
the energy increases
– 1st energy level can hold 2e-1, the 2nd 8e-1, the
3rd 18e-1, etc.
– Further from nucleus = more space = less
repulsion
• Valence shell: the highest-energy occupied
ground state orbit
ni = 3
ni = 3
ni = 2
nf = 2
nn
f =
f =11
Ephoton = ∆E = Ef - Ei
1
Ef = -RH ( 2
nf
1
Ei = -RH ( 2
ni
1
∆E = RH( 2
ni
)
)
1
n2f
)
Problems with the Bohr Model
• Only explains hydrogen atom spectrum (and
other 1-electron systems)
• Neglects interactions between electrons
• Assumes circular or elliptical orbits for
electrons (which is not true)
Wave Mechanical Model of the Atom
• Experiments later showed that electrons
could be treated as waves
– Just as light energy could be treated as particles
– De Broglie
Wave-Particle duality:
λ=h/p=h/mv
h – Planck constant
Louis Victor de Broglie
The Granger Collection
Why is e- energy quantized?
De Broglie (1924) reasoned
that e- is both particle and
wave.
2πr = nλ
λ=
u = velocity of em = mass of e-
h
mu
Wave Mechanical Model of the Atom (cont.)
• The quantum mechanical model treats
electrons as waves and uses wave
mathematics to calculate probability
densities of finding the electron in a
particular region in the atom
– Schrödinger Wave Equation ĤΨ = EΨ
– Can only be solved for simple systems, but
approximated for others
Schrodinger Wave Equation
In 1926 Schrodinger wrote an equation that
described both the particle and wave nature of the eWave function (Ψ) describes:
1. energy of e- with a given Ψ
2. probability of finding e- in a volume of space
Schrodinger’s equation can only be solved exactly
for the hydrogen atom. Must approximate its
solution for multi-electron systems.
Orbitals and Energy Levels
• Solutions to the wave equation give regions
in space of high probability for finding the
electron. These are called orbitals.
• Each principal energy level contains one or
more sublevels. Sublevels are made up of
orbitals.
Figure 11.18: A representation
of the photo of the firefly experiment.
Figure 11.19: The probability map, or orbital, that describes
the hydrogen electron in its lowest possible energy state. The more intense the
color of a given dot, the more likely it is that the electron will be found at that point.
Schrodinger Wave Equation
Ψ = fn(n, l, ml, ms)
principal quantum number n
n = 1, 2, 3, 4, ….
distance of e- from the nucleus
n=1
n=2
n=3
Schrodinger Wave Equation
Ψ = fn(n, l, ml, ms)
angular momentum quantum number l
for a given value of n, l = 0, 1, 2, 3, … n-1
n = 1, l = 0
n = 2, l = 0 or 1
n = 3, l = 0, 1, or 2
l=0
l=1
l=2
l=3
s orbital
p orbital
d orbital
f orbital
Shape of the “volume” of space that the e- occupies
HF/6-31G* electron intracule densities
Critical points of Hartree-Fock/6-31G* electron densities in benzene molecule