electrons
TRANSCRIPT
Electronic Structureof Atoms
What happens when you turn on a neon light?
Electrons in neon atoms, excited to a higher energy level by electricity, emit light when they drop back down to a lower energy.
This is explained by quantum theory
Which describes the behavior of electrons in atoms.
Our current understanding of electronic structure of atoms has come from analysis of light either emitted or absorbed by substances.
Visible light is electromagnetic radiation.
Since Electromagnetic radiation carries energy through space it is called radiant energy.
There are many types of electromagnetic radiation in addition to visible light.
All electromagnetic radiation share one thing.
They all travel at a speed of 3.00 x 108m/s.
The speed of light.
Waves
To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation.
The distance between corresponding points on adjacent waves is the wavelength (λ).
Different forms of electromagnetic radiation have different properties due to different wavelengths.
WavesThe number of waves passing a given point per unit of time is the frequency (ν).
For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.
Electromagnetic Radiation
All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00 108 m/s.
Therefore,
c = λν
Light can be explained as having wave-like properties, but the wave model does not explain several phenomena.The emission of light from hot objects
Blackbody radiation
Emission of electrons from metal surfaces on which light shines
Photoelectric effect
Emission of light from electronically excited gas atoms
Emission Spectra
The Nature of Energy
The wave nature of light does not explain how an object can glow when its temperature increases.
Max Planck explained it by assuming that energy comes in packets called quanta.
Hot objects and the Quantization of EnergyWhen solids are heated they emit radiation.
Red hot iron, Tungsten filament in bulb glows white.
What is the relationship between temperature and the intensity and the wavelengths of the emitted radiation?
In 1900 Max Plank solved the problem by making an assumption:
Energy can be either released or absorbed by atoms only in discrete “chunks” of some minimum size.
Plank gave the name quantum, meaning fixed amount, to the samllest quantity of energy that can be emitted or absorbed as electromagnetic radiation.
He proposed that the energy, E, of a single quantum equals a constant times the frequency of the radiation
E=hv
E=hvh = 6.626 x 10-34 Js
Matter is allowed to emit and absorb energy in whole number multiples of hv.
hv,2hv,3hv, etc.
If the quantity of energy emitted is 3hv, we say that 3 quanta of energy has been emitted.
Because the energy can only be emitted in specific amounts we say the energy is quantized.
Think of a ramp vs. a staircase.
The Nature of Energy
Einstein used this assumption to explain the photoelectric effect.
He concluded that energy is proportional to frequency:
E = hν
where h is Planck’s constant, 6.63 10−34 J-s.
Einstein used Plank’s theory to explain the photoelectric effect.
Light shining on a clean metal surface causes the surface to emit electrons
For each metal there is a minimum frequency below which there are no electrons emitted.
Ex. Light with a frequency of 4.6 X 1014/s or greater will cause cesium to emit electrons
Einstein assumed that the radiant energy striking the metal surface is behaving not like a wave but rather as if it were a stream of tiny energy packets.
He called each energy packet a photon.
The Nature of Energy
Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:
c = λν
E = hν
The Nature of Energy
Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.
The Nature of Energy
One does not observe a continuous spectrum, as one gets from a white light source.
Only a line spectrum of discrete wavelengths is observed.
Not all radiant sources produce a continuous spectrum
Using CRT’s with various gases, they each emit different colors of light
When this light is passed through a prism only a few wavelengths are present
A spectrum containing radiation of only specific wavelengths is called line spectrum.
When scientists first detected the line spectrum of hydrogen, they were fascinated by its simplicity.
Only 4 lines were detected in the visible portion of the spectrum
Johan Balmer showed that the wavelengths of these four visible lines of hydrogen fit a simple formula
Soon Balmer’s equation was extended to a more general one, called Rydberg equation
1/λ= RH ( )1ni2
1nf2
-
where RH is the Rydberg constant, -1.096776 x 107m-1, and ni and nf are positive integers
representing the initial and final energy levels of the electron.
Bohr’s Model
After Rutherford discovered the nuclear nature of the atom scientists thought of the atom as a microscopic solar system in which the electrons orbited the nucleus
So Bohr then started by assuming that the electrons move in circular orbits around the nucleus.
According to classical physics, an electrically charged particle that moves in a circular path should continuously lose energy by emitting electromagnetic radiation and spiral into the nucleus.
Does this happen?
Of course not, hydrogen atoms are stable.
How is it that hydrogen seems to violate these laws?
Bohr approached the problem in the same way Plank did.
Prevailing laws of physics were inadequate in explaining atoms!
He adopted Plank’s idea that energies are quantized.
Bohr based his model on three postulated
Only orbits of certain radii, corresponding to certain definite energies, are permitted for the electron in a hydrogen atom.
An electron in a permitted orbit has a specific energy and is in an allowed energy state. An electron in an allowed energy state will not radiate energy and therefore will not spiral into the nucleus.
Energy emitted or absorbed by the electron only as the electron changes from one allowed energy state to another. This energy is emitted or absorbed as a photon, E = hν
The Nature of Energy
Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:
1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies).
The Nature of Energy
Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:
2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.
The Nature of Energy
Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:
3. Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by
E = hν
The Nature of Energy
The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:
λ = R ( )1ni2
1nf2
-
where R is the Rydberg constant, 109737.31/cm, and ni and nf are the initial and final energy levels of the
electron.
Bohr calculated the energies corresponding to each allowed orbit for the electron in the hydrogen atom
E= (-hcR/n2)
The integer n can have values fro 1 to infinity and is called the principle quantum number
Each orbit corresponds to a different value for n
The radius of the orbit increases as n increases
The energies are negative for all values of n.
The lower (more negative) the energy is, the more stable the atom will be.
The energy is lowest for n=1
As n gets larger it becomes successively less negative
n=1, the lowest energy state, is the ground state.
When electrons are in higher energy states they are in the excited state.
What happens to the radius and the energy as n becomes infinitely large?
Radius increases and electron is separated from the nucleus.
Energy=0.
Bohr postulated that electrons could jump from one energy state to another by absorbing or emitting photons whose radiant energy corresponds exactly to the energy difference between the two states.
The Wave Nature of Matter
Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties.
He demonstrated that the relationship between mass and wavelength was
λ =hmv
Suppose an electron orbiting the nucleus could be thought of not as particles but rather as a wave, with a characteristic wavelength.
He said that the wavelength of the electron depends on its mass and its velocity.
mv is momentum
Therefore any object would give rise to a characteristic matter wave.
Objects with large mass have meaningless wavelengths, but not very small objects.
What is the wavelength of an electron moving with a speed of 5.97 X 106m/s? Mass of an electron is 9.11 x 10-28g
.122nm
The Uncertainty Principle
Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known:
In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!
(Δx) (Δmv) ≥ h4π
Quantum Mechanics
Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated.
It is known as quantum mechanics.
Quantum Mechanics
The wave equation is designated with a lower case Greek psi (ψ).
The square of the wave equation, ψ2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.
Quantum Numbers
Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.
Each orbital describes a spatial distribution of electron density.
An orbital is described by a set of three quantum numbers.
Principal Quantum Number, n
The principal quantum number, n, describes the energy level on which the orbital resides.
The values of n are integers > 0.
Azimuthal Quantum Number, l
This quantum number defines the shape of the orbital.
Allowed values of l are integers ranging from 0 to n − 1.
We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.
Azimuthal Quantum Number, l
Value of l 0 1 2 3
Type of orbital s p d f
Magnetic Quantum Number, ml
Describes the three-dimensional orientation of the orbital.
Values are integers ranging from -l to l:
−l ≤ ml ≤ l.
• Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.
Magnetic Quantum Number, ml
Orbitals with the same value of n form a shell.
Different orbital types within a shell are subshells.
s Orbitals
Value of l = 0.
Spherical in shape.
Radius of sphere increases with increasing value of n.
s Orbitals
Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.
p Orbitals
Value of l = 1.
Have two lobes with a node between them.
d Orbitals
Value of l is 2.
Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.
Energies of Orbitals
For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.
That is, they are degenerate.
Energies of Orbitals
As the number of electrons increases, though, so does the repulsion between them.
Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.
Spin Quantum Number, ms
In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.
The “spin” of an electron describes its magnetic field, which affects its energy.
Spin Quantum Number, ms
This led to a fourth quantum number, the spin quantum number, ms.
The spin quantum number has only 2 allowed values: +1/2 and −1/2.
Pauli Exclusion Principle
No two electrons in the same atom can have exactly the same energy.
For example, no two electrons in the same atom can have identical sets of quantum numbers.
Electron Configurations
Distribution of all electrons in an atom
Consist of
Number denoting the energy level
Electron Configurations
Distribution of all electrons in an atom
Consist of
Number denoting the energy level
Letter denoting the type of orbital
Electron ConfigurationsDistribution of all electrons in an atom.
Consist of
Number denoting the energy level.
Letter denoting the type of orbital.
Superscript denoting the number of electrons in those orbitals.
Orbital Diagrams
Each box represents one orbital.
Half-arrows represent the electrons.
The direction of the arrow represents the spin of the electron.
Hund’s Rule
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”
Periodic Table
We fill orbitals in increasing order of energy.
Different blocks on the periodic table, then correspond to different types of orbitals.
Some Anomalies
Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.
Some Anomalies
For instance, the electron configuration for copper is
[Ar] 4s1 3d5
rather than the expected
[Ar] 4s2 3d4.
Some Anomalies
This occurs because the 4s and 3d orbitals are very close in energy.
These anomalies occur in f-block atoms, as well.