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By the late 1800’s it was clear that classical physics was incapable of describing atoms and molecules

Experiments showed that electrons acted like tiny charged particles in some experiments and waves in others

The physics that describes objects with wave/particle duality is called quantum mechanics or quantum theory

Energy can be transferred between things as light or radiation

Radiation carries energy through space as waves or oscillations moving outward from a disturbance

Electromagnetic waves (radiation) may be characterized by their “height” or amplitude and the number that occur per second or frequency (v)

The units of frequency are the hertz (Hz)

The minimum and maximum amplitude of electromagnetic radiation are evenly spaced

The peak-to-peak distance is called the wavelength

The product of frequency and wavelength give the speed of light (c)

Electromagnetic radiation comes in a broad range of frequencies called the electromagnetic spectrum

The electromagnetic spectrum is divided into regions according to the wavelengths of radiation

What we call light is a small slice of the electromagnetic spectrum with wavelengths between about 400 and 700 nm

This is called the visible region because we can “see” these wavelengths of the electromagnetic spectrum

Gamma rays, X rays, and ultraviolet radiation have wavelengths shorter than the visible region

Microwaves, infrared radiation, and radio waves have wavelengths longer than visible light

The way a substance absorbs electromagnetic radiation can be used to characterize it

For example, each substance absorbs a uniquely different set of infrared frequencies

A plot of wavelengths absorbed versus the absorption is called an infrared absorption spectrum

It can be used to identify a substance

The oscillating magnetic and electric fields of an electromagnetic wave interact with particles that it passes

A charged particle can pick up energy at the expense of the radiation source

The energy transfer is not describe correctly by classical physics

In 1900 the German scientist Max Planck proposed that the electromagnetic radiation could be viewed as a stream of tiny energy packets or quanta we now call photons

Photons travel at the speed of light

Planck proposed, and Einstein confirmed, that the energy of a photon is proportional to its frequency

This means that both electrons and electromagnetic radiation can be represented as either waves or particles

The visible spectrum is a continuous spectrum because it contains a continuous distribution of light of all colors

Excited atoms can emit light

The atomic spectrum or emission spectrum is a series of individual lines called a line spectrum

Atomic spectra are unique for each element

In general, the line spectrum of an element is rather complicated

The line spectrum of hydrogen, with a single electron, is the simplest

The Rydberg equation can be used to calculated all the spectral lines of hydrogen

n1 and n2 are positive integers

The Rydberg constant, RH, is an empirical constant with a value of 109,678 cm-1

Atomic line spectra tells us that when an excited atom loses energy, not just any arbitrary amount can be lost

This is possible if the electron is restricted to certain energy levels

The energy of the electron is said to be quantized

The first theoretical model that successfully accounted for the Rydberg equation was proposed in 1913 by Niels Bohr

Bohr proposed that the electrons moved around the nucleus is fixed paths or orbits much like the planets move around the sun

The orbits, labeled with the integer n, have energy

This equation allows the calculation of the energy of any orbit

The lowest energy state of an atom is called the ground state (an electron with n = 1 for a hydrogen atom)

An electron that “escapes” from the nucleus has infinity for its quantum number and zero energy

Bohr’s (theoretical) equation explains the (empirical) Rydberg equation

The combination of constants, b/hc, has a value which differs from the experimentally derived value of RH by only 0.05%

Bohr’s efforts to develop a general theory of electronic structure was doomed by the wave/particle duality of electrons

De Broglie suggested that the wavelength of a particle of mass m moving at speed v is

This relation provides the link between the description as a particle and as a wave

Heavy objects have very “short” wavelengths so their matter waves and the wave properties go unnoticed

Tiny particles with small masses have “long” wavelengths so their wave properties are an important part of their behavior

Waves combine in two ways

The constructive and destructive interference is called diffraction

Electrons produce similar patterns

There are two types of waves: traveling and standing

A standing wave is produced when a guitar string is plucked: the center of the string vibrates, but the ends remain fixed

Points of zero wave amplitude are called nodes

For guitar strings the only waves are those for which a half-wavelength is repeated exactly a whole number of times

For a strength of length L with n an integer this can be written

These results can be used to show how quantum theory unites the wave and particle description of a bound electron

Consider the classical particle model of the “bead on a wire”

If the electron (particle) has mass m and speed v

The kinetic energy of the moving electron is

The De Broglie relation connects models (a) and (b)

The electron energy is quantized because it depends on the integer n

The lowest energy allowed is for n=1 or E=h2/8mL2 (the energy cannot be zero)

Electrons trapped on a wire have some residual kinetic energy, just like electrons trapped in atoms

The wave that corresponds to the electron is called a wave function

The amplitude of the wave function at a given point can be related to the probability of finding the electron there

According to quantum mechanics there are regions of the wire where the electrons will not be found

Regions of zero wave function amplitude are called nodes

It is generally true that the more nodes an electron has, the higher its energy

Erwin Schrödinger was the first to successfully apply the concept of the wave nature of matter to electronic structure

He developed an equation that can be solved to give wave functions and energy levels for electrons trapped in them

Wave functions for electrons in atoms are called orbitals

Orbitals are characterized by a set of three quantum numbers:

n = principle quantum number. All orbitals with the save principle quantum number are in the same shell. Allowed values: the set of positive integers.

l = secondary quantum number which divides the orbitals in a shell into smaller groups called subshells. Allowed values: from 0 to (n – 1).

ml = magnetic quantum number which divides the subshells into individual orbitals. Allowed values: integers from –l to +l.

The approximate energies of the subshells in an atom with more than one electron:

Electrons behave like tiny magnets

Electrons within atoms interact with a magnet field in one of two ways:

Electron spin is important in determining electronic structure

According to the Pauli exclusion principle no two electrons in the same atom can have identical values for all four quantum numbers

Thus two electron can occupy the same orbital only if they have opposite spin and are said to be paired

A substance with more spin in one direction is said to contain unpaired electrons

Substances with unpaired electrons are slightly attracted to a magnet and are called paramagnetic

Substances in which all electrons are paired are called diamagnetic

The distribution of electrons among the orbitals of an atom is called the electronic structure or electronic configuration

To indicate the ground state electron configuration we can:

List the subshells that contain electrons and indicate their electron population with a superscript.

Represent each orbital with a circle and use arrows to indicate the spin of each electron.

Electron configurations must be consistent with the Pauli principle, aufbau principle, and Hund’s rule

Example: N 1s22s22p3, Na 1s22s22p63s1

Electron configurations explain the structure of the periodic table

There are few important exceptions to the “expected” electronic figurations of commonly encountered elements

Following the rules for Cr, Cu, Ag, and Au using noble gas notation:

Apparently, half-filled and filled subshells are particularly stable

Similar irregularities occur among the lanthanide and actinide elements

The position of an electrons must be described with probabilities

Heisenberg’s uncertainty principle says that it is impossible to measure with complete precision the velocity and position of a particle simultaneously

These limitations are not important for large objects but are very important for small particles like electrons

Quantum mechanics requires that we talk about the probability of finding an electron in a particular region of space

This probability is often represented as an electron cloud about the nucleus

The probability varies with distance from the nucleus

This type of plot shows that electron density varies from place to place

Electron density variations define the shape, size, and orientation of orbitals

p orbitals are quite different from s orbitals

They posses a nodial plane which includes the nucleus and separates the “lobes” of high probability

Recall that there are three different orbitals in each p subshell

The shape and orientation of d orbitals are more complicated than for p orbitals

Shape and directional properties of the five d orbitals in a d subshell.

The f orbitals are even more complex than the d orbital

The amount of positive charge “felt” by outer electrons in atoms other than hydrogen is called the effective nuclear charge

It is lower than the atomic number because of shielding

The effective nuclear charge felt by outer electrons is determined primarily by the difference between the charge on the nucleus and the charge on the core

Effective nuclear charge controls a number of properties

Atomic size increases top to bottom in a group because of increasing n and gets smaller left to right in a groups because the effective nuclear charge increases

Variation in atomic and ionic radii. Values in picometers (10-12 m)

The size trends in ions can be summarized:

Positive ions are always smaller than the atoms they are formed

Negative ions always larger than the atoms from which they are formed

Ionization energy (IE) is the energy required to remove an electron from an isolated, gaseous atom

Successive ionizations are possible until no electrons remain

The trends in IE are the opposite of the trends in atomic size

The electron affinity (EA) is the potential energy change associated with the addition of an electron to a gaseous atom or ion in its ground state

The addition of one electron to a neutral atom is exothermic for nearly all atoms

The addition of more electrons requires energy

Consider the addition of electrons to oxygen:

The results for first electron affinities can be generalized

In general:

EA increases from left to right in a period

EA increases bottom to top in a group

*KIMIA*

Posted on February 25, 20090