Download Chapter 6 Electronic structure of atoms

Chapter 6 Electronic structure of atoms
•
light
•
photons
•
spectra
•
Heisenberg’s uncertainty principle
•
atomic orbitals
•
electron configurations
•
the periodic table
101
F02
Ch6
6.1 The wave nature of light
Visible light is a form of electromagnetic radiation, or radiant energy.
Radiation carries energy through space
1
Electromagnetic radiation can be imagined as a self-propagating
transverse oscillating wave of electric and magnetic fields.
101
F02
Ch6
The number of waves passing a given point per unit of time is the frequency
For waves traveling at the same velocity, the longer the wavelength, the
smaller the frequency.
All electromagnetic radiation travels at the same velocity
The wavelength and frequency of light is therefore related in a
straightforward way:
Blackboard examples
1. what is the wavelength of UV light with ν = 5.5 x 1015 s-1?
2. what is the frequency of electromagnetic radiation that has a wavelength
of 0.53 m?
Wave nature of light successfully explains a range of different phenomena.
2
101
F02
Ch6
Thomas Young’s sketch
of two-slit diffraction of
light (1803)
6.2 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
Hot Objects and the Quantization of Energy
Heated solids emit radiation (blackbody radiation)
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”
The relationship between energy, E, and frequency is:
The Photoelectric Effect and Photons
The photoelectric effect provides evidence for the particle nature of light and
for quantization.
3
Einstein proposed that light could have particle-like properties, which he called
photons.
101
F02
Ch6
Light shining on the surface of a metal can cause
electrons to be ejected from the metal.
Below a threshold frequency
no electrons are ejected
Light has wave-like AND particle-like properties
Blackboard examples
1. MRI body scanners operate with 400 MHz radiofrequency energy. How
much energy does this correspond to in kilojoules/mol?
2. A mole of yellow photons of wavelength 527 nm has __________ kJ of
energy.
6.3 Line Spectra and the Bohr Model
Line spectra
Radiation composed of only one wavelength is called
monochromatic.
When radiation from a light source, such as a light
bulb, is separated into its different wavelength
components, a spectrum is produced,
4
101
F02
Ch6
White light passed through a prism
provides a continuous spectrum
Bohr’s Model
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
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
3. Energy is only emitted or absorbed
by an electron as it moves from one
allowed energy state to another
5
The Energy States of the Hydrogen Atom
101
F02
Ch6
Colors from excited gases arise because
electrons move between energy states in the
atom. Since the energy states are quantized,
the light emitted from excited atoms must be
quantized and appear as line spectra.
Bohr showed mathematically that
where n is the principal quantum number
(i.e., n = 1, 2, 3…) and RH is the Rydberg
constant.
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.
Electrons in the Bohr model can only move between orbits
by absorbing and emitting energy in quanta (E = hν).
The ground state = the lowest energy state
The amount of energy absorbed or emitted by moving between states is given by
Blackboard examples
1. When the electron in a hydrogen atom moves from n = 6 to n = 2, is light
emitted or absorbed?
2. What is its wavelength (in nm)?
6
Limitations of the Bohr Model
101
F02
Ch6
The Bohr Model has several limitations:
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
6.4 The wave behavior of matter
Louis de Broglie posited that if light can have material properties, matter
should exhibit wave properties
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
Matter waves is the term used to describe wave characteristics of material
particles.
7
101
F02
Ch6
Blackboard examples
1. What is the wavelength of a bullet (7.5 g) traveling at 700 ms-1?
2. At what speed must a 3.0 mg object be moving in order to have a
de Broglie wavelength of 5.4 × 10-29 m?
The Uncertainty Principle
Heisenberg’s uncertainty
principle:
The dual nature of matter sets a fundamental limit on how precisely we can
know the location and momentum of an object.
Heisenberg dreamt up the gamma ray
microscope to explain his uncertainty principle.
A source of photons is used to illuminate an
electron fired from the left of the picture. The
position of the electron can be determined from
the scattering of the photons into the telescope
at the bottom right of the picture.
Heisenberg related the uncertainty of the position, ∆x, and the uncertainty in
momentum ∆(mv) to a quantity involving Planck’s constant:
8
6.5 Quantum Mechanics and Atomic Orbitals
101
F02
Ch6
Erwin Schrödinger proposed an equation containing both wave and particle
terms. The solution of the equation is known as a wave function, Ψ (psi), and
describes the behavior of a quantum mechanical object, like an electron.
Ψ2 is called the probability
density. It gives the electron
density for the atom.
Orbitals and quantum numbers
If we solve the Schrödinger equation we get wave functions and corresponding
energies.
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
Blackboard examples
1. Tabulate the relationship among values of n, ℓ and mℓ through n = 4.
9
Orbitals can be ranked in terms of energy; as n
increases energy level spacing becomes smaller.
101
F02
Ch6
6.6 Representations 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 increases
The p orbitals
• p orbitals are dumbell-shaped with two lobes and a node at the nucleus
• 3 values of mℓ, 3 different orientations
The d orbitals
d orbitals have two nodes at the nucleus
10
101
F02
Ch6
• Three of the d orbitals lie in a plane bisecting the x-, y-, and z-axes
• Two of the d orbitals lie in a plane aligned along the x-, y-, and z-axes
• Four of the d orbitals have four lobes each
• One d orbital has two lobes and a collar
6.7 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
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.
11
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 detected:
101
F02
Ch6
Two spots were found: one with the electrons spinning in one direction and one
with the electrons spinning in the opposite direction. Electron spin is quantized:
How do we show spin?
Pauli’s exclusion principle states that:
6.8 Electron Configurations
Electron configurations tell us how the electrons are distributed among the
various orbitals of an atom.
When writing ground-state electronic configurations:
12
101
F02
Ch6
Hund’s Rule
“For degenerate orbitals, the lowest energy is attained when the number of
electrons with the same spin is maximized”
Blackboard examples
1. Draw the electron configurations of Li, Be, B, C, N, O, Ne and Na.
Condensed Electron Configurations
Electron configurations may be written using a shorthand notation (condensed
electron configuration):
1. Write the core electrons corresponding to the noble gas in square brackets
2. Write the valence electrons explicitly
Blackboard examples
1. Draw the condensed electron configurations of Li, Na and P.
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.
13
101
F02
Ch6
6.9 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.
Blocks of elements in periodic table related to which orbital is being filled
Note that the 3d orbitals fill after the 4s orbital. Similarly, the 4f orbitals fill after
the 5s orbitals.
Anomalous Electron Configurations
There are elements that appear to violate the electron configuration guidelines:
When atomic number > 40, energy differences are small and other anomalies
often occur. These usually act to reduce electron repulsions.
14