Download sch4u-quantumtheory

Rise of the Quantum Theory
• Light – particles or waves? Greeks answer:
particles
• 17th century, Christian Huygens, proposed light
can be best described as a wave; Isaac Newton
vehemently opposed
• Mid-19th century, James Maxwell proposed that
light is an electromagnetic wave consisting of
magnetic and electric fields that can exert forces
on an object (Classical Theory of light)
The Wave Nature of Light
Electromagnetic waves originate from the
movement of electric charges
The movement produces fluctuations in electric and
magnetic fields
Characterizing Waves
Electromagnetic radiation is characterized by its
wavelength, frequency, and amplitude
Wavelength (l) is the distance between any
two identical points in consecutive cycles
Characterizing Waves
Frequency of a wave is the number of cycles of
the wave that pass through a point in a unit of time
Amplitude of a wave is its height: the distance
from a line of no disturbance through the center of
the wave peak
The Electromagnetic
Spectrum
The electromagnetic spectrum is largely invisible to the
eye
The Electromagnetic Spectrum
• We can feel some radiation through other
senses (infrared)
• Sunburned skin is a sign of too much
ultraviolet radiation
• Materials vary in their ability to absorb or
transmit different wavelengths
– Our bodies absorb visible light, but transmit
most X rays
– Window glass transmits visible light, but
absorbs ultraviolet radiation
Bright Line & Dark Line Spectra
• Robert Bunsen & Gustav Kirchhoff invented the
spectroscope (1859)
• They found that energized gases emit coloured
light
• Different types of gases emit different colours of
light
• Light from energized elements (gaseous form)
produced specific bands of colour => bright line
or emission line spectrum
• What is a dark line or absorption spectrum?
The Continuous Spectrum
l ~ 650 nm
l ~ 575 nm
l ~ 500 nm
l ~ 480 nm
l ~ 450 nm
The different
colors of light
correspond
to different
wavelengths
and
frequencies
Continuous Spectra
White light
passed
through a
prism
produces a
spectrum –
colors in
continuous
form.
Line Spectra
Light passed
through a prism
from an
element
produces a
discontinuous
spectrum of
specific colors
Line Spectra
The pattern of lines emitted by excited atoms of
an element is unique
= atomic emission spectrum
Key Evidence I – Blackbody
radiation
• Kirchhoff (1859) observed “blackbody”
radiation.
• What is a black body? What is
blackbody radiation?
• Spectrum of the intensity (brightness) of
the radiation yielded a typical bell
curve..SHOCKER
Blackbody Radiation Curves
Actual
Predicted?
Planck’s Interpretation of –
Blackbody Radiation Studies
• Planck (1900) proposed that the vibrating atoms
in a heated solid could absorb or emit
electromagnetic energy only in discrete amounts;
hypothesized that energy is not continuous but
existed in discrete bundles called quanta
•The smallest amount of energy, a quantum, is given by:
E = hv, where h is Planck’s constant: = 6.626 × 10–34 J s
•Planck’s quantum hypothesis states that energy can
be absorbed or emitted only as a quantum or as whole
multiples of a quantum
Key Evidence II –
Photoelectric Effect
•Photoelectric Effect (discovered by Heinrich Hertz; 1887)
= the release of electrons from a metal surface when struck
by light of “appropriate” frequency
•According to classical theory, the intensity of the light
shone on the metal impacts the KE of the liberated
electrons; the photoelectric effect disprove this however
•So what impacted the KE of the liberated electrons?
Einstein’s explanation of the
Photoelectric Effect
• Einstein hypothesized that light was
bundled into little packets called photons
• The energy of a photon can be likened to
the monetary value ascribed to coins
• A photon of red light contained less energy
than a photon of UV light
• Electrons cannot break free unless they
absorb a certain minimum quantity of
energy from a single photon
Bohr’s Hydrogen Atom
Niels Bohr found that the
electron energy (En) was
quantized, that is, that it can
have only certain specified
values
Each specified energy value is
called an energy level of the
atom
The Bohr Model
En = –B/n2 where B is a constant = 2.179 × 10–18 J
and n is an integer
The negative sign represents the forces of attraction
The energy is zero
when the electron is
located infinitely far
from the nucleus
Energy Levels and Spectral
Lines for Hydrogen
Bohr Explains Line Spectra
Bohr’s equation is most useful in determining the
energy change (Elevel) that accompanies the leap
of an electron from one energy level to another
For the final and initial levels:
B
Ef  2
nf
and
B
Ei  2
ni
The energy difference between nf and ni is:
 B   B 
 1 1
E   2    2   B  2  2 
 nf   ni 
 ni nf 
Ground States and Excited
States
Electrons in their lowest possible energy levels are
in the ground state
Electrons promoted to any level n > 1 are in an
excited state
Electrons are promoted by absorbing energy
e.g., electric discharge, heat, lasers (photons)
Electrons in an excited state eventually drop back
down to the ground state  “relaxation”
The Quantum (Wave) Mechanics Model
• In 1924, a French physicist named Louis de Broglie suggested that, like
light, electrons could act as both particles and waves.
• De Broglie's hypothesis was soon confirmed in experiments that showed
electron beams could be diffracted or bent as they passed through a slit
much like light could.
• The waves produced by an electron confined in its orbit about the nucleus
sets up a standing wave of specific wavelength, energy and frequency (i.e.,
Bohr's energy levels) much like a guitar string sets up a standing wave
when plucked.
• De Broglie's vision of Bohr's atom
Quantum (Wave) Mechanics
Quantum mechanics, or wave mechanics, is the
treatment of atomic structure through the wavelike
properties of the electron
Erwin Schrödinger developed an
equation to describe the hydrogen
atom
A wave function is a solution to the
Schrödinger equation and represents
an energy state of the atom
Wave Mechanics = Probability
Wave mechanics provides a probability of where an
electron will be in certain regions of an atom
This region of space where there’s a high probability
of finding an electron is called an orbital
Wave mechanics led to the idea of a “cloud of
electron density” rather than a discrete location
Quantum Numbers and
Atomic Orbitals
A wave function with a given set of these three
quantum numbers is called an atomic orbital
In quantum mechanics the atomic orbitals require
three integer quantum numbers to completely
describe the energy and the shape of the 3-D space
occupied by the electron (n, l, and ml)
Principal Quantum Number (n)
• Is independent of the other two quantum numbers
• Can only be a positive integer
• indicates the size of an orbital (distance from
the nucleus) and its electron energy
• n can be 1, 2, 3, 4, …
Orbital Angular Momentum Quantum
Number (l)
(aka Azimuthal quantum number)
• Determines the shape of the orbital: s, p, d, f , which
corresponds to values l values of: 0, 1, 2, 3
• Possible values of l: 0 to n – 1; e.g. if n = 2, l can only be 0 or 1
• Each of these orbitals is in a different region of space and has a
different shape
•All the ‘l’ quantum values represent different sublevels or
subshells
•When n = 1, there is only one “l” value meaning there is only one
sublevel in the first energy level; when n= 2; there are two values
for ‘l’ indicating two sublevels in the second energy level
Magnetic Quantum Number (ml)
Determines the orientation in space of the orbital;
so named because in a magnetic field, these
different orientations have different energies
Possible values: –l to +l;
e.g., if l = 2,
ml can be –2, –1, 0, 1, 2
The magnetic quantum number, ml, defines the
number of orbitals in a sublevel. E.g. in the l = 0
sublevel, there is only one ml value, therefore there
is only orbital in this sublevel; when l=1; there are 3
possible ml values (-1, 0, +1) 3 orbitals in this
sublevel
Quantum Numbers Summary
Taken together the three quantum numbers specific
the orbital the electron occupies. Namely:
the energy of the orbital, the shape of the orbital, and
the orientation of the orbital
.
• writing 3 quantum numbers to indicate
every possible orbital an electron can
occupy is cumbersome; instead do we do
the following:
– retain the numeric value of the principal
quantum number and use a letter to indicate
the azimuthal quantum number:
l = 0  s; l = 1 p; l = 2  d; l = 3  d
- When combined, they indicate an a
specific orbital e.g. 1s orbital; 2s orbital; 2p
orbital
Radial Distributions
Electrons are most likely to reside nearest the
nucleus because of electrostatic attraction
Probability of finding an electron
decreases as distance (radius) from the
nucleus increases
Electron Probabilities
and the 1s Orbital
The 1s orbital looks very much like a fuzzy ball,
that is, the orbital has spherical symmetry (the
probability of finding an electron is the same in
direction)
The electrons are more concentrated near the center
Electron Probabilities
and the 2s Orbital
The 2s orbital has two regions of high electron
probability, both being spherical
The region near the nucleus is separated from the
outer region by a spherical node - a spherical shell
in which the electron probability is zero
EOS
The Three p Orbitals
-There are three p orbital; each orbital is cylindrically
symmetrical with respect to rotation around one of the
3 axes, x, y, or z
Each ‘p’ orbital has two lobes of high probability
density separated by a node (region of zero
probability)
The Five d Orbitals
Electron Spin (ms)
The electron spin quantum number explains some
of the finer features of atomic emission spectra
The spin refers to a magnetic field induced by the
moving electric charge of the electron as it spins
Only possible values
= –1/2 to +1/2
EOS