Download Chapter 1 Electronic structure of atoms

Chapter 1
Electronic structure of atoms
•
light
•
photons
•
spectra
•
Heisenberg’s uncertainty principle
•
atomic orbitals
•
electron configurations
•
the periodic table
1.1 The wave nature of light
Much of our understanding of the electronic structure of atoms comes from
analyzing light emitted or absorbed by substances
The
electromagnetic
spectrum
Radiation carries energy through space
The visible region
accounts for only a small
portion near the middle
of the electromagnetic
spectrum
Electromagnetic radiation is characterized by its wave nature
Electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave
of electric and magnetic fields.
waves have three characteristics:
peak
Wavelength λ
amplitude
Frequency
v
trough
Amplitude is the height of the wave maximum from the centre.
Wavelength is the distance between successive wave peaks.
wavelength, λ (lambda) has units of distance, m
The number of waves passing a given point per unit of time is the frequency
frequency,
ν (nu) has units of Hertz, s–1
For waves traveling at the same velocity, the longer the wavelength, the smaller the
frequency.
ALL electromagnetic radiation travels at the same velocity:
the speed of light: c = 299,792,458 m/s
~3 × 108 m·s-1
The wavelength and frequency of light are therefore related in a straightforward way:
c = λν
violet light
infrared radiation
ν = 7.50 × 1014 s–1
ν = 3.75 × 1014 s–1
What we perceive as different kinds of electromagnetic energy are waves with
different wavelengths and frequencies.
Interference:
constructive
destructive
Wave nature of light successfully explains a range of different phenomena:
Examples of interference:
stones and ripples, and
reflections from a DVD
Wave model of light useful BUT has some limitations…
1.2 Quantized Energy and Photons
Some phenomena cannot be explained using a wave model of light:
1. Blackbody radiation
2. The photoelectric effect
3. Emission spectra
emission of light from hot objects
emission of electrons from metal surfaces
on which light shines
emission of light from electronically
excited gas atoms
Hot Objects and the Quantization of Energy
Heated solids emit radiation (blackbody radiation):
wavelength distribution depends on
temperature
In 1900, Max Planck investigated black
body radiation, and he proposed that
energy can only be absorbed or
released from atoms in certain
amounts
called “quanta”
A quantum is the smallest amount of
energy that can be emitted or absorbed
as electromagnetic radiation
The relationship between energy, E,
and frequency is:
E = hν
where h is the Planck constant
= 6.626 × 10-34 joule-seconds (Js)
Light
emission
by molten
iron
classical theory =
the “ultraviolet
catastrophe”
T = 7000 K
T = 5000 K
The Photoelectric Effect and Photons
The photoelectric effect (right) provides
evidence for the particle nature of light
and for quantization.
light
electrons
Light shining on the surface of a metal can cause
electrons to be ejected from the metal.
The electrons will only be ejected if the
photons have sufficient energy
Below a threshold frequency no electrons are
ejected.
Above the threshold frequency, the
excess energy appears as the kinetic
energy of the ejected electrons.
Einstein proposed that light could have particle-like properties, which he called
photons.
Energy of one photon = E = hν = h c/λ
Light has wave-like AND particle-like properties
1.3 Line Spectra and the Bohr Model
Line spectra
e.g. laser light
Radiation composed of only one wavelength
is called monochromatic.
a whole array of different wavelengths
is called continuous radiation
When radiation from a light source, such as a light bulb, is
separated into its different wavelength components, a
spectrum is produced. White light passed through a prism
provides a continuous spectrum:
White light
spectrum
Not true of light emitted from excited gaseous elements;
instead, get a line spectrum
Helium spectrum
Discontinuous lines of different colours
Hydrogen lamp
detector
Prism separates
component wavelengths
slit
Lines are characteristic of the element – a “fingerprint”
Rutherford’s model of the atom
Rutherford assumed that electrons orbited the nucleus
analogous to planets orbiting the sun; however, a charged
particle moving in a circular path should lose energy!
→ the atom should be unstable according to Rutherford’s theory!
Hydrogen
spectrum
Bohr’s model of the atom
Niels Bohr noted the line spectra of certain elements and
assumed that electrons were confined to specific energy states.
These he called orbits.
Bohr’s model is based on three postulates:
1. Only orbits of specific radii are
permitted for electrons in an atom
2. An electron in a permitted
orbit has a specific energy
an "allowed" energy state
3. Energy is only emitted or
absorbed by an electron
as it moves from one
allowed energy state
to another
energy is gained or
lost as a photon
these correspond to certain
definite energies
The Energy States of the Hydrogen Atom
Colours from excited gases arise because
electrons move between energy states in the
atom.
since the energy states are quantized, so is
the light emitted from excited atoms
→ appear as line spectra
Bohr showed mathematically that
E = – (hcRH)
1
n2
=
(–2.18 × 10-18 J)
where n is the principal quantum number (i.e., n
= 1, 2, 3…) and RH is the Rydberg constant.
RH = 1.097 × 107 m
The first orbit in the Bohr model has
n = 1 and is closest to the nucleus.
The furthest orbit in the Bohr model has
n = ∞ and corresponds to E = 0.
1
n2
Electrons in the Bohr model can only move between orbits by
absorbing and emitting energy in quanta (E = hn).
The ground state = the lowest energy state
An electron in a higher energy state is said to be in an excited state
The amount of energy absorbed or emitted by moving between states is given by
∆E = Ef – Ei
= hν = hc
λ
=
–2.18 × 10
-18
1
1
–
J
nf2
ni 2
Limitations of the Bohr Model
The Bohr Model has several limitations:
It cannot explain the spectra of atoms other than hydrogen
Electrons do not move about the nucleus in circular orbits
However, the model introduces two important ideas:
1. the energy of an electron is quantized: electrons exist only in certain
energy levels described by quantum numbers
2. energy gain or loss is involved in moving an electron from one energy
level to another.
1.4 The wave behavior of matter
Louis de Broglie suggested that if light can have material properties, matter should
exhibit wave properties
confirmed by the diffraction of a
expected: bright spots
beam of electrons
particle
beam
actual: interference pattern
electron microscopes use electrons
instead of a beam of light
de Broglie proposed that the
characteristic wavelength of the electron
or of any other particle depends on its
mass, m, and on its velocity, v
λ = h / mv
electrons
The momentum, mv, is a particle
property, whereas λ is a wave
property
Matter waves is the term used to describe wave characteristics of material particles.
Applicable to all matter but for objects of ordinary size, the calculated
wavelength is unimaginably short and has no sensible interpretation.
The Uncertainty Principle
Werner Heisenberg:
we cannot determine the exact position,
direction of motion, and speed of
subatomic particles simultaneously
Wave-like AND particle-like
The dual nature of matter sets a limit on how precisely we can know the location and
momentum of an object.
The measuring process interferes with what is being measured
Heisenberg imagined a gamma ray microscope to explain his uncertainty principle.
- photons are used to illuminate an electron
photons
- the position of the electron can be determined
from the scattering of the photons
electrons
- BUT the photon scatters in a random direction
and transfers a large and unknown amount of
momentum to the electron
Heisenberg related the uncertainty of the position, Δx,
and the uncertainty in momentum Δ(mv) to a quantity
involving Planck’s constant:
Δx • Δ(mv) ≥ h / 4π
detector
1.5 Quantum Mechanics and Atomic Orbitals
Erwin Schrödinger proposed an equation containing both wave and particle terms.
The solution of the equation is known as a wave function, Ψ (psi).
describes the behavior of a quantum
mechanical object, like an electron
Ψ2 is the probability density
Ψ2 gives the electron density for the atom
A region of high electron density =
high probability of finding an electron
Schrödinger treated electrons in the
hydrogen atom as standing waves
Higher energy standing
waves have nodes
Orbitals and quantum numbers
If we solve the Schrödinger equation we get wave functions and corresponding
energies.
These wave functions are called orbitals
The probability density (or electron density) described by an orbital has a characteristic
energy and shape. The energy and shape of orbitals are described by three quantum
numbers. These arise from the mathematics of solving the Schrödinger equation.
the principal quantum number, n
must be a positive integer n = 1,2,3,4,…
the angular momentum quantum number, ℓ
maximum value is (n-1), i.e. ℓ = 0,1,2,3…(n-1)
use letters for ℓ (s, p, d and f for ℓ = 0, 1, 2, and 3).
the magnetic quantum number, mℓ
maximum value depends on ℓ, can take integral
values from – ℓ to + ℓ
mℓ = (-ℓ),…,0,…,(+ ℓ)
describes the main energy level;
specifies electron shell
describes the shape;
specifies subshell
designates specific orbital;
specifies orientation
Orbitals can be ranked in terms of energy.
Orbital energy levels in the hydrogen atom
as n increases energy level spacing
becomes smaller
each cluster of boxes = one subshell
each row = one shell
n = 3 shell has three subshells composed of nine orbitals
n = 2 shell has two subshells composed of four orbitals
n = 1 shell has one orbital
each box = one orbital
1.6 Representations of Orbitals
The s orbitals
node = probability of
finding an electron is 0
For all orbitals the number of nodes is
given by n – 1
• All s orbitals are spherical
• As n increases, the s orbitals get larger
• As n increases, the number of nodes increases
height of graph
indicates
electron
probability at a
single point at
distance r
height of graph
indicates electron
probability density
per volume of a
“shell”
The p orbitals
p orbitals are dumbell-shaped
3 values of mℓ
two lobes and a nodal plane at the nucleus
3 different orientations
pz
px
py
3 representations of electron probability for 2pz orbital
The d orbitals
d orbitals have two nodal planes (well, most do. Some nodes are not planes.)
5 values of mℓ so
5 different orbitals with
different orientations
xy plane
3 d orbitals have lobes that lie between the x-, y-, and z-axes
2 d orbitals have lobes that lie aligned along the x-, y-, or z-axes
4 of the d orbitals have 4 lobes each
1 d orbital has 2 lobes and a “donut”
Electrons in the Bohr model can only move between orbits by
absorbing and emitting energy in quanta (E = hn).
The ground state = the lowest energy state
An electron in a higher energy state is said to be in an excited state
The amount of energy absorbed or emitted by moving between states is given by
∆E = Ef – Ei
= hν = hc
λ
=
–2.18 × 10
-18
1
1
–
J
nf2
ni 2
Limitations of the Bohr Model
The Bohr Model has several limitations:
It cannot explain the spectra of atoms other than hydrogen
Electrons do not move about the nucleus in circular orbits
However, the model introduces two important ideas:
1. the energy of an electron is quantized: electrons exist only in certain
energy levels described by quantum numbers
2. energy gain or loss is involved in moving an electron from one energy
level to another.
1.7 Many-Electron Atoms
Orbitals and Their Energies
In a many-electron atom, for a given value of n,
the energy of an orbital increases with
increasing value of ℓ
Orbitals of the same energy are
said to be degenerate
For n ≥ 2, the s and p orbitals are
no longer degenerate
Therefore, the energy-level diagram looks
slightly different for many-electron systems
Electron Spin and the Pauli Exclusion Principle
Line spectra of many-electron atoms show each line as a closely spaced pair of lines.
Wolfgang Pauli postulated that electron must exist in two states
Stern and Gerlach designed an experiment to determine why. A beam of atoms was
passed through a slit and into a non-homogeneous magnetic field and the atoms were
Beam
detected:
collector
Magnet
Two spots were found,
plate
corresponding to silver
atoms with electrons in
different states. (Note that
Slit
silver atoms have one
unpaired electron each.)
Beam splits
in two
Beam of
atoms
we define a 4th quantum number
ms = spin magnetic quantum number =
±½
electron “spin” is
quantized
How do we show these
two states?
ms = + ½ (spin up)
ms = – ½ (spin down)
Pauli’s exclusion principle states that:
- no two electrons can have the same set of four quantum numbers
- therefore, two electrons in the same orbital must have opposite spins
i.e. ms=+1/2 and ms=-1/2
1.8 Electron Configurations
Electron configurations tell us how the electrons are distributed among the various
orbitals (energy levels) of an atom.
The most stable configuration, or ground state, is that in which the
electrons are in the lowest possible energy state
When writing ground-state electronic configurations:
- electrons fill orbitals in order of increasing energy
- no two electrons can fill one orbital with the same spin (Pauli)
H
1s 1
He
1s 2
Li
1s 2 2s 1
Quantum numbers are like postal codes
Hund’s Rule
“For degenerate orbitals, the lowest energy is attained when the number of electrons
with the same spin is maximized”
- electrons fill each orbital singly with their spins parallel before any orbital
gets a second electron
- electron-electron repulsions are minimized
Condensed Electron Configurations
Electron configurations may be written using a shorthand notation:
1. Write the core electrons corresponding to the noble gas in square brackets
= electrons in the inner shells; generally not involved in bonding.
2. Write the valence electrons explicitly
= electrons in the outer shell; those gained or lost in reactions
Transition Metals
After Ca the 3d orbitals begin to fill
The block of the periodic table in which the d orbitals are filling represents the transition
metals.
The Lanthanides and Actinides
Elements 57-70 are the lanthanides (“rare earths”) in which the 7 degenerate 4f orbitals fill:
Actinides are
5f elements
89-102
usually put under the rest of the PT
1.9 Electron Configurations and the Periodic Table
The periodic table can be used as a guide for electron configurations.
the period number is the value of n
s-block
alkali and
alkaline
earth
metals
d-block
transition metals
p-block
main
group
elements
f-block
lanthanides and actinides
Blocks of elements in periodic table relate to which orbital is being filled
- the 4s orbital fills before the 3d orbitals
- the 6s orbital fills before the 4f orbitals (which fill before the 5d orbitals)
Anomalous Electron Configurations
There are elements that appear to violate the electron configuration guidelines:
e.g.
Cr [Ar] 3d 5 4s 1 not [Ar] 3d 4 4s 2
Cu [Ar] 3d 10 4s 1 not [Ar] 3d 9 4s 2
- due to special stability of half-filled and filled shell configurations
When atomic number > 40, energy differences are small and other anomalies often
occur. These usually act to reduce electron repulsions.
Summary of rules
Aufbau - German for “building up”
We can collect these rules for adding electrons to orbitals under the useful umbrella
known as the “Aufbau Principle”. We apply them in the following order:
1. Lower energy orbitals fill with electrons first
2. Any orbital can hold up to 2 electrons. If there are two electrons in the
same orbital, they have opposite spins (Pauli Exclusion Principle).
3. If two or more degenerate orbitals are available, one electron goes into
each until all are half-filled, then they start pairing up (Hund’s rule).
4. A particularly stable configuration is one in which a set of p or d orbitals
is either filled or half-filled (e.g. Cr, Cu)