Electromagnetic Radiation is one of the forces that carry energy.
Electromagnetic Radiation includes visible and invisible light, ranging from gamma rays, X rays, Ultraviolet light, visible light, infrared heat, microwaves, radio waves, etc.
Electromagnetic Radiation's main characteristic is that of a wave.
Electromagnetic Radiation strongly interacts with electrons and allows to probe properties of atoms and molecules
The distance between two consecutive peaks or troughs in a wave.
The number of waves (cycles) that pass a given point in space in a second.
Since all Electromagnetic Radiation travels at the same speed (the speed of light, c), a long wavelength will have a low frequency. a short wavelength will have a high frequency.
Wavelength and frequency are inversely related. Specifically,
ln = c
c is the speed of light, 2.9970 x 108 m/s
n has the units of s-1 (1/s)
l has the units of meters
Electromagnetic Radiation is quantized in that it can exist in only discrete quantities.
For a system absorbing or emitting Electromagnetic Radiation, the change in energy is represented by
DE = nhn
where n is an integer representing the number of quanta, and h is Planck's constant
h = 6.626 x 10-34 J s (kg m2/s)
an experimental value
The fundamental unit of electromagnetic radiation is the photon. All interactions involve whole numbers of photons, no fractions of photons are ever observed. The photon is both a wave and a particle.
The energy of a photon has the value of
E = hn = hc/l
Planck's Equation
The energy of a photon is proportional to the frequency and inversely proportional to the wavelength.
Based on Einstein's well known equation, we see that light also has mass. Combining the above two equations we get
m = E/c2 = (hc/l)/c2 = h/lc
All matter and energy "waves" consist of wave-particles, items that behave as both particles and waves.
Waves are decentralized and exist in a smeared, multiple location existence. Particles occur in only one place at one time and have a finite, limited extent.
Wave nature occurs more when we do not look and particle nature occurs more when we look.
A Continuous Spectrum contains all the frequencies/colors of visible light
A Line Spectrum contains discrete lines of light at particular wavelengths.
The hydrogen emission spectrum is a line spectrum showing that only certain energies are allowed for the electron in the hydrogen atom. The energy levels in the hydrogen atom are quantized.
Good Aspects
Electrons exist only in certain discrete energy levels,
which are described by quantum numbers, and
Energy is involved in moving an electron from one level to another.
Failed Aspects
Electrons circle the nucleus at fixed distances.
The electron in a hydrogen atom moves around the nucleus in only certain allowed circular orbits and certain allowed angular momentum values (product of mass, velocity, and orbital radius).
The energy levels of an electron in a hydrogen atom are
E = (-hcRH)(1/n2) = -2.18 x 10-18 J(1/n2)
where; n is an integer (principal quantum number)
h is Planck's constant
c is speed of light
RH is Rydberg constant
The lowest energy state (n = 1) is called the ground state.
The electron in any other state (n = 2 or greater) is called an excited state.
The energy is negative since the energy of an electron is defined to be zero when it is infinitely separated from the atom (n = ¥). The negative energy means that the electron is stable around the atom.
The energy is negative in any orbit.
A more negative value is more tightly bonded electron.
The Ground State is the lowest possible energy state for an electron. It is n = 1 for the hydrogen electron.
The energy associated with the transfer of an electron between energy levels is
DE = Efinal – Einitial
Where Efinal and Einitial are calculated using E = -2.178 x 10-18 J(Z2/n2)
For the hydrogen atom this can be expressed as
DE = -2.178 x 10-18 J(1/nf2 - 1/ni2)
A negative energy change means energy is released
A positive energy change means energy is absorbed
The wavelength of the emitted photon can be calculated using
E = hn = hc/l
or
l = hc/DE
Some substitution of the above equations can give us the Rydberg Equation:
1/l = RH(1/nf2 - 1/ni2)
Which describes the wavelengths of the line spectrum of the hydrogen atom.
The energy required to remove an electron from the hydrogen atom can be calculated using n = ¥ for the final state
The wavelength of matter can be calculated from a re-arranged version of the above equation where the velocity, v, is used instead of the speed of light.
l = h/mv
This is called de Broglie's equation
What does de Broglie Wavelength mean???
Macroscopic objects have small de Broglie Wavelength's that are not yet observable. Small particles have larger de Broglie Wavelength's which have been experimentally verified.
There is a fundamental limitation to how precisely we can know both the position and momentum of a particle at a given time. This is represented mathematically by
Dx D(mv) > h/4p
The more accurately we know position, the less accurately we know momentum and vice versa.
h = 6.626 x 10-34 Js
As was shown, the electron is a wave.
The electron forms a standing wave around the nucleus. The standing wave does not move and results from a stable constructive overlay of the wave around the nucleus.
The mathematical treatment of this concept results in Schrodinger's equation
Hy = Ey
Where H is a mathematical function called an operator
and, y is the wave function, a representation of the electrons position in space
and E is the total (potential and kinetic) energy of the atom
Many solutions are found for this equation. Each solution has a particular value of E. Each solution is called an orbital.
The square of the wave function (y2) indicates the probability of finding in a particular area of space.
Probability Distribution
A representation of the probability of finding an electron in space by using a probability density map.
The many solutions to the Schrodinger equation are each characterized by a series of numbers called quantum numbers, which describe various properties of the orbital.
The Principal Quantum Number (n) has integer values.
n = 1, 2, 3, 4, ….
The Principal Quantum Number is related to the size and energy of the orbital. As n increases, the orbital becomes larger and has a higher energy (less negative) and is not held as strongly by the nucleus.
The Angular Momentum Quantum Number (l) has integer values from 0 to n-1 for each value of n.
l = 0, 1, 2, …, n-1
The value of l
is commonly assigned a letter
l = 0, s
l = 1, p
l = 2, d
l = 3, f
These are referred to as subshells
The Magnetic Quantum Number (ml) has integer values between l and -l
-l, -l+1, …, 0, …, l-1, l
The value of ml is related to the orientation of the orbital in space relative to the other orbitals in the atom
The Electron Spin Quantum number (ms) can only have one of two values , 1/2 and –1/2
The Electron Spin Quantum number corresponds to a magnetic moment that has two possible orientations.
Electrons will align with or against an external magnetic field, thus the electron has a magnetic moment, which could be considered as caused by a spinning electric charge.
The Electron Spin Quantum number represents the rotational symmetry of the electron.
Each shell will have n subshells.
Each subshell will have 2l+1 orbitals.
Each shell will have n2 orbitals.
An Orbital is a specific wave function corresponding to a specific energy level.
An orbital does not have a specific radius, and we do not know how the electron moves around the nucleus.
A probability distribution corrected to show the density of the electron as a function of radius (probability of finding the electron at a particular radius)
The size of the surface that contains 90% of the electron density, an arbitrary decision.
A node is a surface of zero probability density separating areas of nonzero probability density. The node separate areas of different phase signs of the electron.
There are two common ways to graphically represent an orbital. A probability distribution, or a surface that contains 90% of the electron density.
The s orbitals are spherical, with the surface representation being larger as n increases. The probability distribution will also show nodal surfaces, or nodes in the 2s, 3s, 4s, etc. A nodal surface is an area of zero probability separating areas of nonzero probability.
The 1s has no nodes, the 2s has 1 node separating 2 areas of nonzero density, the 3s has 2 nodes separating 3 areas of nonzero density, etc.
The 2p orbitals contain two lobes separated by a node at the nucleus.
The 3p orbital contains additional nodes through the two previous lobes, creating 4 areas of nonzero density.
The 3d orbitals have two different fundamental shapes four of the orbitals (dxz, dyz, dxy, and dx2-y2) have four lobes centered in the plane indicated by the orbital label. The dz2 orbital has a unique shape with two lobes along the z axis and a doughnut shaped ring in the xy plane.
The 4f orbitals come in two varieties, four of the orbitals contain 8 lobes. Three of the orbitals contain two lobes aligned along an axis with two doughnut shaped lobed around the base of each of the axis lobes.
In the hydrogen atom the energy of the orbitals is determined only by the value of n. So all orbitals with the same value of n have the same energy and are called degenerate.
In many-electron atoms, for a given value of n, the energy of an orbital increases with increasing values of l.
An electron in the lowest possible energy orbital is said to be in the ground state.
An electron in a higher energy orbital than the ground state is said to be in an excited state.
In a polyelectronic atom, the wave function/Schrodinger equation cannot be solved analytically, it is usually solved iteratively, or by using approximations.
The shapes of the orbitals of these atoms resemble the shapes of the hydrogen atom orbitals; however, the sizes and energies are different. For a given principal quantum number, the orbitals are not all the same energy and vary as
Ens < Enp < End < Enf
The electron behaves as if it is a spinning charged object, creating a magnetic moment. The actual physical meaning of this is unclear.
ms has values of –1/2 or +1/2
The meaning of the value 1/2 is that the electron has a rotational symmetry of 1/2, so it takes two full rotations before it is identical to its starting position.
A person has a rotational symmetry of 1, and an equilateral triangle has a rotational symmetry of 3 (in one full rotation it has three positions that look identical)
In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, ms)
So;
An orbital can hold only two electrons, each with opposite spins.
The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals.
By convention these are shown to have parallel up spins
The electrons in the outermost principal quantum level of an atom
The electrons occupying the inner principal quantum levels
Energy levels are filled
from the lowest energy to the highest.
However, some sublevels are of higher energy than sublevels of the next
main level. The order of levels (increasing energy) are:
1s < 2s
< 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
< 4f* < 5d < 6p < 7s < 5f* < 6d < 7p
* the d series starts, then
the f series fills out before the d series finishes.
Electron configuration is shorthand notation to show what electron levels
are filled with electrons
The notation consists of
the energy level, sublevel, and a superscript of the number of electrons in
that level
These are listed together
from the lowest energy up to the highest occupied energy level
Examples:
H 1s1
Be 1s2
2s2
Al 1s2
2s2 2p6 3s2 3p1
Sc 1s2
2s2 2p6 3s2 3p6 4s2 3d1
Zr 1s2
2s2 2p6 3s2 3p6 4s2 3d10
4p6 5s2 4d2
Ta 1s2
2s2 2p6 3s2 3p6 4s2 3d10
4p6 5s2 4d10 5p6 6s2 4f14
5d3
Pm 1s2
2s2 2p6 3s2 3p6 4s2 3d10
4p6 5s2 4d10 5p6 6s2 4f4
5d1
Note: In promethium (Pm),
two sublevels are partially filled
The electron configuration
of an element can be written in shorthand notation by representing the inner
core electrons by the symbol of the preceding noble gas.
Example:
Sc 1s2 2s2
2p6 3s2 3p6 4s2 3d1
the noble gas preceding scandium is Argon,
Ar 1s2 2s2
2p6 3s2 3p6
So Scandium can be represented by
Sc [Ar] 4s2 3d1
Note: the electron
configuration of noble gas ends with p6 except for Helium, which is
1s2
Cores are
He 1s2
Ne 1s2
2s2 2p6
Ar 1s2
2s2 2p6 3s2 3p6
Kr 1s2
2s2 2p6 3s2 3p6 4s2 3d10
4p6
Xe 1s2
2s2 2p6 3s2 3p6 4s2 3d10
4p6 5s2 4d10 5p6
Rn 1s2
2s2 2p6 3s2 3p6 4s2 3d10
4p6 5s2 4d10 5p6 6s2 4f14
5d10 6p6
118? 1s2
2s2 2p6 3s2 3p6 4s2 3d10
4p6 5s2 4d10 5p6 6s2 4f14
5d10 6p6 7s2 5f14 6d10
7p6
Orbital diagrams give similar information to electron configurations, except that they represent the electrons as arrows in a box representing the orbital.
Each orbital holds two electrons. In an orbital diagram, when the orbital is full, the two electrons are represented by two arrows, one up, and one down. The direction of the arrow represents a properties of electrons called electron spin, which is labeled either up or down.
Pauli Exclusion Principle states that the two electrons in an orbital have to have opposing spins.
When orbitals are incompletely filled; follow Hund's Rule, which states that when filling orbitals of equal energy, fill them singly with parallel spins first.
The A column elements, groups 1,2, and 13-18, These have their top electron in either an s or p orbital.
The B column elements, groups 3-12, these have their top electron in a d orbital
We can predict electron configuration for most transition elements based on location in periodic table. However, some movement of electrons from the s orbital to the d orbitals occurs especially when this results in the d orbitals being fully occupied with either 1 or 2 electrons.
The first inner-transition (f-transition) row. The top electron is in a 4f orbtital. There is some movement of an electron between the d sublevel and the f sublevel.
The second inner-transition (f-transition) row. The top electron is in a 5f orbtital. There is some movement of an electron between the d sublevel and the f sublevel.
Groups of elements exhibit similar chemical properties that change in a regular way
Each group member has the same valence electron configuration
It is the number and type of valence electrons that primarily determine an atom's chemistry.
Electron configurations can be read from the position of an element in the table.