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Electronic Structure
of Atoms
electronic structure: the arrangement of
electrons in an atom
quantum mechanics: the physics that correctly
describes atoms
?
electromagnetic radiation (i.e., light)
-- waves of oscillating electric (E)
and magnetic (B) fields
-- source is… vibrating electric charges
E
B
Characteristics of a Wave
crest
amplitude A
trough
wavelength l
frequency: the number of cycles per
unit time (usually sec)
-- unit is Hz, or s–1
electromagnetic spectrum: contains all of the “types” of
light that vary according to frequency and wavelength
750 nm
400 nm
-- visible spectrum ranges from
only ~400 to 750 nm (a very
narrow band of spectrum)
cosmic rays
gamma rays
X-rays
UV
low energy
visible
low f
IR
microwaves
radio waves
large l
ROYGBV
small l
high f
high energy
Albert Michelson (1879)
-- first to get an accurate
value for speed of light
Albert Michelson
(1852–1931)
The speed of light in
a vacuum (and in air)
is constant:
c = 3.00 x 108 m/s
-- Equation:
c=nl=fl
In 1900, Max Planck assumed
that energy can be absorbed
or released only in certain
discrete amounts, which he
called quanta.
Later, Albert Einstein dubbed
a light “particle” that carried a
quantum of energy a photon.
-- Equation:
Max Planck
(1858–1947)
E=hn=hf
E = energy, in J
h = Planck’s constant
= 6.63 x 10–34 J-s (i.e., J/Hz)
Albert Einstein
(1879–1955)
A radio station transmits
at 95.5 MHz (FM 95.5).
Calculate the wavelength
of this light and the energy
of one of its photons.
c 3.00 x 108 m/s
c=fl  l =
= 3.14 m
6
95.5 x 10 Hz
f
E = h f = 6.63 x 10–34 J/Hz (95.5 x 106 Hz)
=
6.33 x 10–26 J
In 1905, Einstein explained the photoelectric effect
using Planck’s quantum idea.
-- only light at or above a threshold freq. will
cause e– to be ejected from a metal surface
ROYGBV
e–e–
– e– e–
e
e– e– e– e –
e– e– e–
light source
e– e–
e– e – e–
metal surface
Frequency (i.e., energy)
of light determines IF e–
are ejected or not, and
with what KE.
Intensity/brightness of
light determines
HOW MANY e– are
ejected.
Einstein also expanded Planck’s idea, saying that
energy exists only in quanta.
Light has both wavelike and particle-like qualities,
and... so does matter.
?
Line Spectra
Ordinary white light
is dispersed by a
prism into a...
“continuous” spectrum.
From the gas in a nearly-evacuated gas-discharge
tube, we instead get a... line spectrum.
H2 absorption spectrum
H2 emission spectrum
(if the H2 is absorbing
light from an
external source)
(if the H2 has been
energized and is
emitting light)
Niels Bohr took Planck’s
quantum idea and applied
it to the e– in atoms.
-- e– could have only
certain amounts of
energy
-- e– could be only at
certain distances from
nucleus
planetary
(Bohr)
model
e–
found
here
Niels Bohr
(1885–1962)
N
e– never
found here
-- Bohr assumed that the e– in his circular orbits
had particular energies, given by:
1
En   RH  2 
n 
RH = Rydberg constant
= 2.18 x 10–18 J
n = 1, 2, 3, ... (the principal
quantum number)
The more/less (–) an
i.e., the energy level
electron’s energy is...
the more/less stable the atom is.
“barely”
(if at all)
(–) E
When n is very large, En “barely”
e– - - - - - - - -0- - - - - - - - stable
goes to zero, which is the
energy “well”
–
most energy an e– can have
e
“a bit”
because…zero is larger “a bit” (–) E
stable
e– very stable
than anything (–). (e– has
very (–) E
escaped completely from atom.)
-- Bohr stated that e– could move from one level to
another, absorbing light of a particular freq. to
“jump up” and releasing light of a particular freq.
to “fall down.”
He: 1s12 2s1
EMITTED ENERGY
LIGHT
(HEAT, LIGHT,
ELEC., ETC.)
-- Bohr’s model (i.e., its specific equation) worked
only for atoms with… a single e–.
Find the wavelength, frequency,
and energy of a photon of the
1
 
En   RH  2 
emission line produced when an
n 
e– in a hydrogen atom makes the
transition from n = 5 to n = 2.
For n = 5…
18  1 
E5   2.18 x 10  2  = –8.72 x 10–20 J
5 
For n = 2…
E2 = –5.45 x 10–19 J
DE = 4.58 x 10–19 J = energy of photon
E
 4.58 x 1019 J
14 Hz
E=hf  f 
=
6.91
x
10
h 6.63 x 1034 J/Hz
c 3.00 x 108 m/s
c=fl  l 
= 4.34 x 10–7 m
14
f 6.91 x 10 Hz
The Wave Behavior of Matter
Since light (traditionally thought of
as a wave) was found to behave as
both a wave and a particle, Louis de
Broglie suggested that matter
(traditionally thought of as particles)
might also behave like both a wave
and a particle. He called these…
Louis de Broglie
(1892–1987)
matter waves.
-- The wavelength of a moving
sample of matter is given by:
h
h
l 

p
mv
m = mass (kg)
v = speed (m/s)
A proton moving at 1200 m/s would
be associated with a matter wave
of how many nanometers?
In the absence of further info…
1g

 1 kg 

mp ~ 1 amu 

23
 6.02 x 10 amu  1000 g 
= 1.66 x 10–27 kg
(actual p+ mass
is ~1.673 x 10–27 kg)
h
6.63 x 1034 J/Hz
l

mv
(1.66 x 1027 kg) (1200 m/s)
= 3.3 x 10–10 m
= 0.33 nm
 1 nm 


9
 1 x 10 m 
A wave is smeared out through space, i.e., its location
is not precisely defined. Since matter exhibits wave
characteristics, there are limits to how precisely we
can define a particle’s (e.g., an e–’s) location.
-- the limitation also applies to a particle’s...momentum
-- Heisenberg’s uncertainty principle:
It is impossible to know simultaneously
BOTH the exact momentum of a particle
AND its exact location in space.
h
Dx  D(mv ) 
4
D = “uncertainty in”
h = Planck’s const.
(It is inappropriate to imagine an e– as a
solid particle moving in a well-defined orbit.)
Werner Heisenberg
(1901–1976)
Schrodinger’s wave equation (1926) accounts for
both wave and particle behaviors of e–.
   2Y  2Y  2Y 
Y

 2  2  V Y  i 
2

2m  x
y
z 
t
w/no
where
h-bar
is the of
reduced
Planck’s
constant
(=h/2),
V is the
potential
energy,
Y iselectric
the
wave
function)
(for a non-relativistic
particle
mass and
m
charge
and zero spin,
-- Solutions to the wave equation
yield wave functions, symbolized
by Y, which have no physical
meaning, but Y2 at any point in
space gives the probability that
you’ll find an e– at that point. Y2
is called the probability density,
which gives the electron density.
Erwin Schrodinger
(1887–1961)
-- Orbitals describe a specific distribution of electron
density in space.
Each orbital has a characteristic shape and energy.
(“Not.”)
(Well, theory says that there
ARE g orbitals, but they
don’t look like this.)
WeThe
alsolanthanides
think g orbitals
andcontain
they look
like this…
and exist,
actinides
f orbitals.