Download Modern Atomic Theory Notes

ELECTRONS IN ATOMS
SHORTCOMINGS OF RUTHERFORD’S MODEL
Rutherford’s Nuclear Model did not explain how the atom’s electrons are arranged around the nucleus
No explanation on why negatively charged electrons are not pulled into the atom’s positively charged
nucleus
Nuclear model did not account for the differences in chemical behavior among various elements
ELECTROMAGNETIC RADIATION
James Maxwell developed an elegant mathematical theory in 1864 to describe all forms of radiation in
terms of oscillating or wave-like electric and magnetic fields in space.
PROPERTIES OF LIGHT
Wave Description of Light
Electromagnetic Radiation
Form of energy that
exhibits
Electromagnetic Spectrum
All forms of
electromagnetic
radiation which include
gamma rays, X-rays,
ultraviolet, infrared ,
visible light, microwaves,
and radio waves
All EM Radiation travel at a speed of 3 x 108 m/s
PROPERTIES OF WAVES
WAVELENGTH (λ - lambda)
Unit:
FREQUENCY (ν - nu)
Unit:
AMPLITUDE
Height of the wave from
CHEMISTRY Page 1 of 10 WAVELENGTH & FREQUENCY
Wavelength is __________________________ to frequency
WAVE EQUATION
c = λν
where
c
λ
ν
ν =
=
=
=
c
λ
λ=
c
ν
speed of light constant (3.00 x 108 m/s)
wavelength (m, cm, nm)
frequency (Hz, 1/s, s-1)
WAVE/FREQUENCY CALCULATIONS
1. What is the frequency of green light which has a wavelength of 4.90 x 10-7 m ?
2.
What is the wavelength of electromagnetic radiation having a frequency of 5.00 x 1012 Hz?
3.
A popular radio station broadcasts with a frequency of 94.7 MHz. What is the wavelength of the broadcast?
PLANCK’S QUANTUM CONCEPT
Max Planck (1900)
Suggested that hot objects emit energy in small specific amounts called quanta
Quantum –
PLANCK’S EQUATION
E = energy (J)
c
h = Planck’s constant (6.62 x 10-34 J-s)
E = hc
=
ν = frequency (1/s, s-1, Hz)
c = speed of light constant
8 = wavelength
Energy ____________________________ to frequency
ν
λ
E=
hc
λ
ENERGY & FREQUENCY CALCULATION
1.What is the energy of a photon of red light having a frequency of 4.48 x 1014 Hz?
CHEMISTRY Page 2 of 10 2. A photon has an energy of 2.93 x 10-23 J. What is its frequency?
3. What is the energy of an ultraviolet photon having a wavelength of 1.18 x 10-8 m?
4. A photon has an energy of 1.10 x 10-13 J. What is the photon’s wavelength?
PHOTOELECTRIC EFFECT
Emission of electrons from a metal when light shines on the metal
Wave theory predicted that light of any frequency could supply enough energy to eject an electron
(which did not happen)
Wave Model could not explain photoelectric effect
Scientists could not explain why the light had to be of a minimum frequency
(Threshold Frequency) in order for the photoelectric effect to occur
Albert Einstein (1905)
Used the Planck’s equation to explain photoelectric effect
Explained that light has a dual wave-particle nature
Photon –
Electromagnetic radiation is absorbed by matter in _______________________
Electrons in different metals are bound more or less tightly, so different metals require different
minimum frequencies to exhibit photoelectric effect
Arthur Compton & Photons (1922)
Performed experiments on X-Ray and electron collision
Determined the mass of photon
SPECTROSCOPY
Ultraviolet Radiation has such a high energy, it violently excites electrons
Visible Radiation are not as destructive because it has less energy
Transition of the electrons from normal state to such highly excited state cause changes in
molecules, useful in studying the substances
Infrared Spectroscopy is also useful when studying whole molecules
SPECTRUM
CHEMISTRY Page 3 of 10 EMISSION SPECTRA
Continuous Spectrum
NOT QUANTUM
ATOMIC or LINE EMISSION SPECTRUM
Series of specific wavelengths of emitted light created when visible portion of light from excited atoms is
shined through a prism
Consists of fine lines of individual colors
Atomic or Line Emission Spectrum can be used as a "fingerprint" for an element
QUANTUM
HYDROGEN ATOM LINE-EMISSION SPECTRUM
Hydrogen atoms do not give off a continuous spectrum!
Indicates that the energy difference between the atom’s energy states were fixed
Also suggests that the electron of a hydrogen atom exists only in specific energy states
Attempts to explain the hydrogen spectrum led to the development of Quantum Mechanical Model
BOHR MODEL OF THE ATOM
Niels Bohr (1913)
Planetary Model of the Atom
Linked atom’s electron with photon emission
Explained why excited hydrogen gas gives off
certain colors of light
When energy is put into an atom,
When an atom emits energy, electrons fall from higher
energy orbits (excited state) to lower energy orbits
(ground state), giving off light (photon)
The energy (and therefore the wavelength) of the
emitted light
LINE SPECTRA arise from the transitions between discrete
(quantized) energy states
Quantized –
SUMMARY
Electrons are arranged in concentric circular paths or orbits, around the nucleus
Electrons in a particular path have a fixed energy , thus they do not lose energy and fall into the
nucleus
Energy Level –
MAJOR DEFECTS IN BOHR’S THEORY
Only works for Hydrogen atom
Did not explain the spectra of atoms with more than one electron
Secondly, the electron DOES NOT orbit the nucleus in a fixed path!!
Did not explain the chemical nature of matter
CHEMISTRY Page 4 of 10 QUANTUM MODEL OF THE ATOM
Classical (Newtonian) Mechanics
Energy is gained or lost in any amount
Quantum Mechanics
Particles gain or lose energy in packages called quanta
Erwin Schrodinger, Louie de Broglie and Werner Heisenberg focused on the wave properties of the
electron
They treated the electron as a “standing wave” – stationary
Davisson & Germer at Bell Lab (1927) observed diffration patterns when electron beams were directed at
a Ni crystal
Patterns show results of bent waves that have interfered with each other
Bright areas correspond to areas of increased energy (constructive interference)
Dark areas correspond to areas of decreased energy (destructive interference)
This proves that electrons, which are particles, have wavelength associated with them
WAVE-PARTICLE DUALITY PROPERTY
Louis de Broglie (1925)
Wave-Particle Duality
De Broglie Equation
Combined Einstein’s and Planck’s equations
Predicted that all matter exhibits wavelike motion
ALL PARTICLES HAVE WAVE PROPERTIES & ALL WAVES HAVE PARTICLE PROPERTIES
λ = wavelength of the particle
h
h = Planck’s constant
λ
=
m = mass of the particle
mv
v = velocity of the particle
DE BROGLIE’S EQUATION
1. Compare the wavelength for an electron (mass = 9.11 X 10-31 kg) traveling at a speed of 1.0 X 107 /s with
that for a ball (mass = 0.10 kg) traveling at 35 m/s.
HEISENBERG UNCERTAINTY PRINCIPLE
It is impossible to determine accurately both position and velocity of an electron or any other particle
Because h is constant, Δp &Δx are inversely proportional
The more certain we are of the location, the less certain we are of its momentum
h
ΔpΔx ≥
4π
CHEMISTRY Δp – uncertainty in momentum Δx – uncertainty in location h – Planck’s constant Page 5 of 10 SCHROEDINGER’s WAVE EQUATION
Formulated mathematical equations to find
Equation tells us about the shape and orientations of the probability distribution of the electrons
Each solution describes a possible energy state for the electrons in atoms
EACH SOLUTION IS DESCRIBED BY A SET OF QUANTUM NUMBERS
PROBABILITY DISTRIBUTION
Radial probability distribution
QUANTUM MODEL
QUANTUM THEORY
QUANTUM MECHANICAL MODEL
Electrons are treated as waves and makes no attempt to describe electron’s path
QUANTUM NUMBERS
Numbers that describe the energies of electrons in atoms
Specify the properties of atomic orbitals and the properties of electrons in orbitals
Think of the quantum numbers as addresses for electrons
FOUR QUANTUM NUMBERS
Principal Quantum Number (n)
Angular Momentum Quantum Number (l )
Magnetic Quantum Number (ml)
Spin Quantum Number (s )
PRINCIPAL QUANTUM NUMBER
Indicates the main energy level occupied by the electron
Can take on integer values n = 1, 2, 3,…. 4
Largely determine the energy of the orbital
(bigger n value = higher energy)
All electrons in an atom with the same value of n belong to the
same shell
CHEMISTRY Page 6 of 10 ANGULAR MOMENTUM QUANTUM NUMBER
Also known as
Indicates the shape of the orbital within a shell
Only integer values between 0 and n-1 are allowed
Affects orbital energies (bigger l = higher energy)
All electrons in an atom with the same value of l are said
to belong to the same subshell
Sometimes called the azimuthal quantum number
MAGNETIC QUANTUM NUMBER
Does not affect orbital energy (except in magnetic fields!)
Only integer values between –l and +l are allowed
The number of ml values within a subshell is the number of orbitals within a subshell
SPIN QUANTUM NUMBER
Spin makes the electron behave like tiny magnets
Spin can be clockwise or counterclockwise
Spin quantum numbers can have values of +½ or -½
ATOMIC ORBITALS
Region in space where there is a high probability of finding an electron
Shapes
s–
p–
d & f – complex shapes
Special People Don’t Forget 1, 3, 5, 7
CHEMISTRY Page 7 of 10 ELECTRON CONFIGURATION
An arrangement of electrons in an atom
GROUND STATE –
EXCITED STATE – a state in which an atom has a higher
potential energy
DEGENERATE ORBITALS –
ELECTRON ARRANGEMENT DETERMINES THE
CHEMICAL BEHAVIOR OF ATOMS
AUFBAU PRINCIPLE
PAULI EXCLUSION PRINCIPLE
No two electrons can have
An atomic orbital contains a
HUND’S RULE
Orbitals of equal energy are each occupied by
Electrons in singly occupied orbitals must have the same spins
REPRESENTING ELECTRON CONFIGURATIONS
ORBITAL NOTATION –orbital is represented by a line, with the orbital’s name written under the line
and the electrons are represented by arrows.
ELECTRON CONFIGURATION NOTATION
Carbon: 1s22s22p2
HIGHEST OCCUPIED LEVEL
Electron-containing main energy level with the highest principal quantum number
VALENCE ELECTRONS
INNER SHELL (CORE) ELECTRONS
CHEMISTRY Page 8 of 10 NOBLE GAS NOTATION
Na:
P:
Noble Gas Configuration
An outer main energy level fully occupied, in
most cases, by eight electrons (octet)
Ne: 1s22s22p6
Ar: [Ne] 3s23p6
Magnetism & Electron Spin
Diamagnetic: NOT attracted to a magnetic field.
Diamagnetic – not magnetic
In fact, they are slightly repelled.
All electrons are
Opposite spins—magnetic fields cancel.
Paramagnetic – attracted to a magnetic field
Lose their magnetism when removed from the magnetic field
Ferromagnetic – retain magnetism upon introduction to, then removal from a magnetic field
Electron Configurations: Metals vs. Nonmetals
Metals
Valence electrons in
A few heavy elements have atoms with one or two electrons in p sublevels
Nonmetals
Valence electrons in
Nonmetals starting with period 3 and higher can have expanded octet (more than 8 electrons in its
outermost level) since d orbital becomes available starting with the 3rd main energy level
There are more metals than nonmetals because filling d orbitals in a given energy level involves the atoms
of ten elements and filling the f orbitals involves the atoms of 14 elements.
In the same energy levels, the maximum number of elements with atoms receiving p electrons is six
EXCEPTIONS TO RULES
Half filled orbitals - Cr24
1s22s22p63s23p6 4s2 3d4
] [[[[p
Stable configuration is
1s22s22p63s23p6 4s1 3d5
[ [[[[[
CHEMISTRY Page 9 of 10 Filled Orbitals - Cu29
1s22s22p63s23p6 4s2 3d9
] ]]]][
Stable configuration is
1s22s22p63s23p6 4s1 3d10
[ ]]]]]
QUANTUM NUMBERS & ATOMIC ORBITALS
ISOELECTRONIC SPECIES
Any combination of two ions or an atom and an ion are isoelectronic if
As a result they must be distinguished by some other means, for example the number of protons present.
CHEMISTRY Page 10 of 10