Transcript Electronic Structure of Atoms

Electronic Structure of Atoms
Chapter 6
Introduction
• Almost all chemistry is driven by electronic
structure, the arrangement of electrons in
atoms
• What are electrons like?
• Our understanding of electrons has
developed greatly from quantum
mechanics
6.1 Wave Nature of Light
• If we excite an atom, light can be emitted.
• This nature of this light is defined by the
electron structure of the atom in question
– light given off by H is different from that by
He or Li, etc.
– Each element is unique
6.1 Wave Nature of Light
• The light that we can see (visible light) is only
a small portion of the “electromagnetic
spectrum”
• Visible light is a type of “electromagnetic
radiation” (it contains both electric and
magnetic components)
• Other types include radio waves, x-rays, UV
rays, etc. (fig. 6.4)
The Wave Nature of Light
The Wave Nature of Light
• All waves have a characteristic
wavelength, l, and amplitude, A.
• The frequency, n, of a wave is the
number of cycles which pass a
point in one second.
• The speed of a wave, v, is given
by its frequency multiplied by its
wavelength: For light, speed = c.
c = nl
c vs. l vs. n
• The longer the wavelength, the fewer cycles are
seen
• c=lxn
• radio station KDKB-FM broadcasts at a
frequency of 93.3 MHz. What is the wavelength
of the radio waves?
Quantized Energy and Photons
• Classical physics says that changes occur
continuously
• While this works on a large, classical theories
fail at extremely small scales, where it is found
that changes occur in discrete quantities, called
quanta
• This is where quantum mechanics comes into
play
Quanta
• We know that matter is quantized.
– At a large scale, pouring water into a glass
appears to proceed continuously. However, we
know that we can only add water in increments of
one molecule
• Energy is also quantized
– There exists a smallest amount of energy that can
be transferred as electromagnetic energy
Quantization of light
• A physicist named Max Planck proposed that
electromagnetic energy is quantized, and
that the smallest amount of electromagnetic
energy that can be transferred is related to
its frequency
Quantization of light
• E = hn
– h = 6.63 x 10-34 J.s (Planck's constant)
– Electromagnetic energy can be transferred in
inter multiples of hn. (2hn, 3hn, ...)
• To understand quantization consider the notes
produced by a violin (continuous) and a piano
(quantized):
– a violin can produce any note by placing the
fingers at an appropriate spot on the bridge.
– A piano can only produce notes corresponding
to the keys on the keyboard.
Photoelectric effect
• If EM radiation is shined upon a clean metal
surface, electrons can be emitted
• For any metal, there is a minimum frequency below
which no electrons are emitted
• Above this minimum, electrons are emitted with
some kinetic energy
• Einstein explained this by proposing the existence
of photons (packets of light energy)
– The Energy of one photon, E = hν.
Quantized Energy and Photons
The Photoelectric Effect
Sample
• Calculate the energy of one photon of
yellow light whose wavelength is 589 nm
Sample Problems
• A violet photon has a frequency of 7.100 x 1014
Hz.
– What is the wavelength (in nm) of the photon?
– What is the wavelength in Å?
– What is the energy of the photon?
– What is the energy of 1 mole of these violet photons?
Free Response Type
Question
• Chlorophyll a, a photosynthetic pigment
found in plants, absorbs light with a
wavelength of 660 nm.
– Determine the frequency in Hz
– Calculate the energy of a photon of light with
this wavelength
Bohr’s Model of the Hydrogen Atom
Radiation composed of only one wavelength is called
monochromatic.
•Radiation that spans a whole array of different wavelengths is
called continuous.
•White light can be separated into a continuous spectrum of
colors.
•If we pass white light through a prism, we can see the
“continuous spectrum” of visible light (ROYGBIV)
•Some materials, when energized, produce only a few distinct
frequencies of light
•neon lamps produce a reddish-orange light
•sodium lamps produce a yellow-orange light
These spectra are called “line spectra
Bohr’s Model of the Hydrogen Atom
Line Spectra
Shows that visible light contains many
wavelengths
Bohr’s Model of the Hydrogen Atom
Bohr’s Model
Colors from excited gases arise because electrons move
between energy states in the atom.
Only a few wavelengths emitted from elements
Bohr’s Model of the Hydrogen Atom
Bohr’s Model
Since the energy states are quantized, the light emitted
from excited atoms must be quantized and appear as
line spectra.
After lots of math, Bohr showed that
E = (-2.18 x 10-18 J)(1/n2)
Where n is the principal quantum number (i.e., n = 1, 2, 3, ….
and nothing else)
“ground state” = most stable (n = 1)
“excited state” = less stable (n > 1)
When n = ∞, E = 0
Bohr Model
• To explain line spectrum of hydrogen, Bohr proposed that
electrons could jump from energy level to energy level
– When energy is applied, electron jumps to a higher energy level
– When electron jumps back down, energy is given off in the form of light
– Since each energy level is at a precise energy, only certain amounts of
energy (DE = Ef – Ei) could be emitted
– I.e.
D E  E f  E i  hn
 1
1 
E photon  hn  RH  
n 2  n 2 

 lower
upper 
Bohr’s Model of the Hydrogen Atom
Bohr’s Model
We can show that
DE = (-2.18 x 10-18 J)(1/nf2 - 1/ni2 )
When ni > nf, energy is emitted.
When nf > ni, energy is absorbed.
Sample calculation (Free
Response Type Question)
• In the Balmer series of hydrogen, one spectral line
is associate with the transition of an electron from
the fourth energy level (n=4) to the second energy
level n=2.
– Indicate whether energy is absorbed or emitted as the
electron moves from n=4 to n=2. Explain (there are no
calculations involved)
– Determine the wavelength of the spectral line.
– Indicate whether the wavelength calculated in the
previous part is longer or shorter than the wavelength
assoicated with an electron moving from n=5 to n=2.
Explain (there are no calculations involved)
Wave Behavior of Matter
• EM radiation can behave like waves or particles
• Why can't matter do the same?
• Louis de Broglie made this very proposal
– Using Einstein’s and Planck’s equations, de Broglie
supposed:
h
l
mv
What does this mean?
• In one equation de Broglie summarized the
concepts of waves and particles as they
apply to low mass, high speed objects
• As a consequence we now have:
– X-Ray diffraction
– Electron microscopy
Sample Exercise
• Calculate the wavelength of an electron
traveling at a speed of 1.24 x 107 m/s.
The mass of an electron is 9.11 x 10-28 g.
The Uncertainty Principle
Heisenberg’s Uncertainty Principle: on the mass scale
of atomic particles, we cannot determine the exactly the
position, direction of motion, and speed simultaneously.
For electrons: we cannot determine their momentum
and position simultaneously.
Quantum
Orbitals
Mechanics
and
Atomic
•Schrödinger proposed an equation that contains both
wave and particle terms.
•Solving the equation leads to wave functions.
•The wave function gives the shape of the electronic
orbital.
•The square of the wave function, gives the probability
of finding the electron, that is, gives the electron density
for the atom.
Quantum
Orbitals
Mechanics
and
Atomic
Quantum
Orbitals
Mechanics
and
Atomic
If we solve the Schrödinger equation, we get wave
functions and energies for the wave functions.
We call wave functions orbitals.
Schrödinger’s equation requires 3 quantum numbers:
Principal Quantum Number, n. This is the same as Bohr’s n.
As n becomes larger, the atom becomes larger and the
electron is further from the nucleus.
Orbitals and Quantum Numbers
Azimuthal Quantum Number, l. Shape This quantum
number depends on the value of n. The values of l
begin at 0 and increase to (n - 1). We usually use
letters for l (s, p, d and f for l = 0, 1, 2, and 3).
Usually we refer to the s, p, d and f-orbitals.
Magnetic Quantum Number, ml direction This
quantum number depends on l. The magnetic
quantum number has integral values between -l and
+l. Magnetic quantum numbers give the 3D
orientation of each orbital.
Orbitals and Quantum Numbers
Sample Exercise
• Which element (s) has an outermost
electron that could be described by the
following quantum numbers (3, 1, -1, ½ )?
You Try
• Which element (s) has an outermost
electron that could be described by the
following quantum numbers (4, 0, 0, ½)
Quantum
Orbitals
Mechanics
and
Atomic
Orbitals can be ranked in terms of energy to yield an
Aufbau diagram.
Note that the following Aufbau diagram is for a single
electron system.
As n increases, note that the spacing between energy
levels becomes smaller.
Representation of Orbitals
The s Orbitals
All s-orbitals are spherical.
As n increases, the s-orbitals get larger.
As n increases, the number of nodes increase.
A node is a region in space where the probability of
finding an electron is zero.
At a node, 2 = 0
For an s-orbital, the number of nodes is (n - 1).
Representation of Orbitals
The s Orbitals
Representation of Orbitals
The p Orbitals
There are three p-orbitals px, py, and pz. (The three p-orbitals lie
along the x-, y- and z- axes. The letters correspond to allowed
values of ml of -1, 0, and +1.)
The orbitals are dumbbell shaped.
As n increases, the p-orbitals get larger.
All p-orbitals have a node at the nucleus.
Representation of Orbitals
The p Orbitals
Representation of Orbitals
The d and f Orbitals
There are 5 d- and 7 f-orbitals.
Three of the d-orbitals lie in a plane bisecting the x-, y- and zaxes.
Two of the d-orbitals lie in a plane aligned along the x-, y- and zaxes.
Four of the d-orbitals have four lobes each.
One d-orbital has two lobes and a collar.
Representation of Orbitals
The d Orbitals
F Shape of f orbitals
Orbitals in Many Electron Atoms
Orbitals of the same energy are said to be
degenerate.
All orbitals of a given subshell have the same
energy (are degenerate)
For example the three 4p orbitals are degenerate
Orbitals in Many Electron Atoms
Energies of Orbitals
Orbitals in Many Electron Atoms
Electron Spin and the Pauli Exclusion Principle
•Line spectra of many electron atoms show each line as a closely
spaced pair of lines.
•Stern and Gerlach designed an experiment to determine why.
•A beam of atoms was passed through a slit and into a magnetic
field and the atoms were then detected.
•Two spots were found: one with the electrons spinning in one
direction and one with the electrons spinning in the opposite
direction.
Orbitals in Many Electron Atoms
Electron Spin and the Pauli Exclusion Principle
Orbitals in Many Electron Atoms
Electron Spin and the Pauli Exclusion Principle
Since electron spin is quantized, we define ms = spin
quantum number =  ½.
Pauli’s Exclusions Principle: no two electrons can have
the same set of 4 quantum numbers.
Therefore, two electrons in the same orbital must have
opposite spins.
Electron Configurations
Electron configurations tells us in which orbitals the
electrons for an element are located.
Three rules:
•electrons fill orbitals starting with lowest n and
moving upwards
•no two electrons can fill one orbital with the same
spin (Pauli)
•for degenerate orbitals, electrons fill each orbital
singly before any orbital gets a second electron
(Hund’s rule).
Details
• Valence electrons- the electrons in the
outermost energy levels (not d).
• Core electrons- the inner electrons.
• C 1s2 2s2 2p2
Fill from the bottom up
following the arrows
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
• 1s2 2s2 2p6 3s2
3p6 4s2 3d10 4p6
5s2 4d10 5p6 6s2
56
• 38
20electrons
4212
Electron Configurations and the Periodic
Table
Electron Configurations and the Periodic
Table
There is a shorthand way of writing electron configurations
Write the core electrons corresponding to the filled Noble gas in
square brackets.
Write the valence electrons explicitly.
Example, P: 1s22s22p63s23p3
but Ne is 1s22s22p6
Therefore, P: [Ne]3s23p3.
Exceptions
• Ti = [Ar] 4s2 3d2
• V = [Ar] 4s2 3d3
• Cr = [Ar] 4s1 3d5
• Mn = [Ar] 4s2 3d5
• Half filled orbitals.
• Scientists aren’t sure of why it happens
• same for Cu [Ar] 4s1 3d10
More exceptions
• Lanthanum La: [Xe] 6s2 5d1
• Cerium Ce: [Xe] 6s2 4f1 5d1
• Promethium Pr: [Xe] 6s2 4f3 5d0
• Gadolinium Gd: [Xe] 6s2 4f7 5d1
• Lutetium Lu: [Xe] 6s2 4f14 5d1
Diamagnetism and Paramagnetism
• Diamagnetism
– Repelled by magnets
– Occurs in elements
where all electrons are
paired
– Usually group IIA or
noble gases
• Paramagnetism
– Attracted to magnets
– Occurs in elements
with one or more
unpaired electrons
– Most elements are
paramagnetic