# week 2 notes.docx

7/28/2019 # Week 2 Notes.docx

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ELECTROMAGNETIC RADIATION

(

)

Energy that is transmitted, or radiated, through space in the form of electric and magnetic fields is known

as electromagnetic radiation, or light. All forms of electromagnetic radiation consist of perpendicular

oscillating electric and magnetic fields:

All electromagnetic waves travel at the same speed in vacuum, the speed of light:

THE QUANTIZATION OF ENERGY


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Energy can be gained or lost only in integral multiples of the smallest unit of energy, a quantum.

BLACKBODY RADIATION

The ultraviolet catastrophe (decrease in radiation intensity energy per unit of area of heated objects in

the ultraviolet range) can be explained as follows. At low temperatures, radiation with only relatively low

frequencies is emitted, corresponding to low-energy quanta. As the temperature of an object increases,

there is an increased probability of emitting radiation with higher frequencies, corresponding to higher-

energy quanta. At any temperature, however, it is simply more probable for an object to lose energy by

emitting n lower-energy quanta than a single very high-energy quantum that corresponds to ultraviolet

radiation.

THE PHOTOELECTRIC EFFECT

Radiant energy of light arrives at the metal surface in particles called photons, each possessing a particular

energy . Each metal has a particular electrostatic attraction for its electrons (binding energythe amount of energy required to free electrons from their atomic orbits, also known as ionization energy)

that must be overcome before an electron can be emitted from its surface ( ). If photons oflight with energy less than strike a metal surface, no single photon has enough energy to eject anelectron, so no electrons are emitted regardless of the intensity of the light. If a photon with energy greaterthan strikes the metal, then part of its energy is used to overcome the forces that hold theelectron to the metal surface, and the excess energy appears as the kinetic energy of the ejected electron:


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When a metal is struck by light with energy above the threshold energy the numberof emittedelectrons is proportional to the intensityof the light beam, which corresponds to the number of photons

per square centimetre, but the kinetic energy of the emitted electrons is proportional to the frequency

(and, hence, the energy) of the light.

THE BOHR MODEL AND ATOMIC SPECTRA

Zis the atomic number which is the number of protons in an atom.

Each proton has a charge equal to the elementary charge:


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means that it takes positive energy to pull the electron away from the proton and ultimately reachzero energy (free electron). The binding energy, therefore, is positive and the opposite of the above

expression.

The orbit with is the lowest in energy (binding energy is highest). The most stable arrangement ofelectrons in an atom is one with the lowest possible energy and is called the ground state. When an atom

in an excited state ( ) undergoes a transition to the ground state in a process called decay, it losesenergy ( ) by emitting a photon whose energy corresponds to the difference in energy between thetwo states:

||

The above equation describes the light frequencies of photons emitted by atoms returning from an excited

state () to the ground state (), where and are positive integers representing electron orbits (withsmaller being lower energy orbits) and .The change in energy is negative and indicates that energy is released as the electron moves from orbit to orbit because orbit is at a higher energy than orbit .

Key implications of the Bohr model:

Electrons can occupy only certain regions of space called orbits.


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Orbits closer to the nucleus are lower in energy (energy is negative, which means it takes more energyto pull electrons away from the proton the closer they are to it).

Electrons can move from one orbit to another by absorbing (to move further away from the proton) oremitting (to move closer) energy, giving rise to the characteristic absorption spectra and emission

spectra.

WAVE-PARTICLE DUALITY

Depending on conditions, light could be viewed as either a wave or a particle. This condition is known as

wave-particle duality:

Small particles such as electrons can be described by a wave whose wavelength is given by

where is the Planck constant, is the mass of the particle and is the velocity of the particle.Objects with larger masses have such short wavelengths that they are best regarded primarily as particles.

In contrast, objects with very small masses (such as photons) have large wavelengths and can be viewed

primarily as waves. Objects with intermediate masses, such as electrons, exhibit properties of both particles

and waves.

STANDING WAVES

A standing wave is a wave that does not travel in space. An example is the motion of a string of a violin or

guitar. When a string is plucked, it vibrates at certain fixed frequencies because it is fastened at both ends.

If the length of the string is , then the lowest-energy vibration (the fundamental) has wavelength: Higher energy vibrations (overtones) are produced when the string is plucked more strongly. They have

wavelengths given by:

where is any positive integer. Thus the vibrational energy of the string is quantized, and only certainwavelengths and frequencies are possible. If , then the wave has nodes points where the stringdoes not move. The amplitude of the wave at a node is zero.

Two-dimensional surfaces, such as a drumhead, also have quantized vibrations. When the ends of a string

are joined to form a circle, the only allowed vibrations are those which dont cause destructive

interference. They have wavelength of:


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Bohrs allowed orbits could be understood if the electron behaves like a standing circular wave. The

standing wave could exist only if the circumference of the circle was an integral multiple of the wavelength

such that the propagated waves were all in phase, thereby increasing the net amplitudes and causing

constructive interference (overlapping exactly with themselves). With any other radii, the propagatedwaves would be out of phase, resulting in a net decrease in amplitude and causing destructive interference.

At the lowest energy level orbit ( ), one complete wavelength would close the circle. Higher energylevels would have successively higher values of with a corresponding number of nodes.

THE HEISENBERG UNCERTAINTY PRINCIPLE

Because a wave is a disturbance that travels in space, it has no fixed position. One might therefore expect

that it would also be hard to specify the exact position of a particle that exhibits wavelike behaviour.

Heisenberg stated that at every moment the electron has only an inaccurate position and an inaccuratevelocity, and between those two inaccuracies there is this uncertainty relation. Mathematically, the

Heisenberg uncertainty principle states that the uncertainty in the position of a particle ( ) multiplied bythe uncertainty in its momentum () is greater than or equal to Plancks constant divided by : Because Plancks constant is such a small number, the Heisenberg uncertainty principle is important only

for particles that have very low masses, such as electrons. These are the same particles predicted by de

Broglies equation to have measurable wavelengths.

The more accurately we know the position of a particle ( ), the more uncertain its momentum is().

WAVE FUNCTIONS

A wave function () is a mathematical function that relates the location of an electron at a given point in

space (identified byx, yand z coordinates) to the amplitude of its wave, which corresponds to its energy.

The square of the wave function at a given point is proportional to the probability of finding an electron at

that point, which leads to a distribution of probabilities in space. We use probabilities because according to

Heisenbergs uncertainty principle, we cannot precisely specify the position of an electron.


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QUANTUM NUMBERS

Quantum numbers provide information about the spatial distribution of an electron.

1) The principal quantum number (n) tells the average relative distance of an electron from the nucleus:

A value of signifies that the electron exists in the lowest energy state and its orbit is theinnermost allowed shell, as close to the nucleus as possible. All wave functions that have the same

value of are said to constitute a principal shell because those electrons have similar averagedistances from the nucleus.

2) The second quantum number is the azimuthal quantum number (). The value of describes the shapeof the region of space occupied by the electron. It specifies the angular momentum of orbitingelectrons and, to a minor extent, their energy.


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For a given atom, all wave functions that have the same values of both and form a subshell. Theregions of space occupied by electrons in the same subshell usually have the same shape, but they are

oriented differently in space.

3) The third quantum number, called the magnetic quantum number (), controls the number ofallowed spatial orientations of each orbit characterized by in a given shell (characterized by ). Forparticular values of and : Each wave function with an allowed combination of, and values describes an atomic orbital, aparticular spatial distribution of electrons. For a given set of quantum numbers, each principal shell has

a fixed number of subshells, and each subshell has a fixed number of orbitals.

Example:

n l Subshell Designation Orbitals in Subshell Orbitals in Shell3 0 3s 0 1 9

1 3p -1, 0, 1 3

2 3d -2, -1, 0, 1, 2 5

DEGENERACY

When orbitals have the same energy (same ), this is called degeneracy. For any , the degeneracy level is.


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ATOMIC ORBITALS

Wave mechanics asserts that an electron in an atom cannot be considered as a particle having an orbit with

a definite radius. Instead, there is a probability of an electron being at certain spatial positions. Hence, the

location of an electron is best described in terms of its probability density distribution, which is sometimes

called an electron cloud.

Radial probability is the probability of finding a electron on a spherical shell at a distance from thenucleus. 52.9 pm is the most probable radius for the electron in the ground state ( ) of the hydrogenatom and is the same as the Bohr radius.


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Three things happen to orbitals as increases:1) The orbitals become larger, extending farther from the nucleus.2) They contain more nodes. This is similar to a standing wave that has regions of significant amplitude

separated by nodes (points with zero amplitude).

3) For a given atom, the orbitals also become higher in energy as increases because of their increaseddistance from the nucleus.


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EFFECTIVE NUCLEAR CHARGE

For an atom with only a single electron, we can calculate the potential energy by considering only the

electrostatic attraction between the positively charged nucleus and the negatively charged electron. When

more than one electron is present, however, the total energy of the atom depends also on repulsive

electron-electron interactions.

If an electron is far from the nucleus (large ), then at any given moment, most of the other electrons willbe between that electron and the nucleus. Hence the inner electrons will cancel a portion of the positive

charge of the nucleus and thereby decrease the attractive interaction between it and the electron farther

away. As a result, the electron farther away experiences an effective nuclear charge () that is less thanthe actual nuclear charge

. This effect is called electron shielding.

As the distance between an electron and the nucleus approaches infinity, approaches a value of 1because all the other ( ) electrons in the neutral atom are, on average, between it and the nucleus. If,on the other hand, an electron is very close to the nucleus, then at any given moment most of the other

electrons are farther from the nucleus and do not shield its charge. At , the positive chargeexperienced by an electron is approximately the full nuclear charge ( ). At intermediate values of, .Within a given principal shell of a multielectron atom, the orbital energies increase with increasing . Theseenergy differences are caused by the effects of shielding and penetration, the extent to which a given

orbital lies inside other filled orbitals.


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ELECTRON SPIN: THE FOURTH QUANTUM NUMBER

4) When an electrically charged object spins, it produces a magnetic moment parallel to the axis ofrotation, making it behave like a magnet. The fourth quantum number, called the electron spin

quantum number (), can be interpreted as the direction of the magnetic moment of an orbitingelectron.

The positive value represents parallel spin (), the negative is anti-parallel spin ().

ELECTRON CONFIGURATION

The Pauli Exclusion Principle states that in any atom no two electrons may have the same four quantum

numbers. From this principle it follows that each electronic orbital can accommodate at most two electrons

differing by their spin quantum number. The Pauli principle is based on the fact that the separate existence

of any electron depends upon its non-destruction by interference, i.e. on its wave nature.

The build-up of the electronic states of an atom is obtained by placement of the electrons in the orbitals of

the lowest energy first. The quantum states for electrons follow the Aufbau Principle that the lowest , and numbers are selected first by electrons in multi-electron atoms. Each orbital can hold two electrons,one with spin up, corresponding to , which is arbitrarily written first, and one with spin down,corresponding to . A filled orbital is indicated by , in which the electron spins are said to bepaired. The number of electrons in each subshell is indicated by a superscript following the name of the

subshell (1s1

for hydrogen, 1s2

for helium, 1s22s

1for lithium and so on).

At carbon, with Z= 6 and six electrons, we are faced with a choice. Should the sixth electron be placed in

the same 2p orbital that already has an electron, or should it go in one of the empty 2p orbitals? If it goes in


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the empty orbital, what should be its spin? Because of electron-electron repulsions, it is more favourable

energetically for an electron to be in an unoccupied orbital. The spin of the electrons is described by Hunds

rule, which says that the lowest-energy electron configuration for an atom is the one that has the

maximum number of electrons with parallel () spins in degenerate orbitals.

For carbon, electrons are placed in unoccupied 2p orbitals with parallel spin. For oxygen, since all 2p orbitals already have one electron each and since each electron has parallel

spin, the last electron must have anti-parallel spin and it can be in any 2p orbital.

For neon, as for helium, all the orbitals through 2p level are completely filled.Chemists simplify the notation by using a bracketed noble gas symbol to represent the configuration of the

noble gas from the preceding row because all the orbitals in a noble gas are filled. For example, [Ne]

represents the 1s22s

22p

6electron configuration, so the electron configuration of sodium, which is

1s22s

22p

63s

1, is written as [Ne]3s

1.

Because electrons in filled inner orbitals are closer to the nucleus and more tightly bound to it, they are

rarely involved in chemical reactions. This means that the chemistry of an atom depends mostly on the

electrons in its outermost shell, which are called the valence electrons. The simplified notation allows us to

see the valence-electron configuration more easily.


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PERIODIC TRENDS

Although the table of elements was originally organized on the basis of physical and chemical similarities

between the elements within groups, these similarities are ultimately attributable to orbital energy levels

and the Pauli principle, which cause the individual subshells to be filled in a particular order.

As a result, the periodic table can be divided into blocks corresponding to the type of subshell that is being

filled. Within each column, each element has the same valence electron configuration.


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ATOMIC RADII

AsZincreases, the most inner shells experience stronger nuclear charge, therefore, the energy of the filled

inner orbitals is lower (they are more stable), and the peaks for nsorbitals radial probability distribution

are closer to the nucleus with increasing Z. The difference in causes differences in atomic radiibecause of its effect on the radial probability distribution of outermost orbitals.

Elements with more effective electron shielding have larger atomic radii. Electrons in the same principalshell (in the same row of the periodic table) are not very effective at shielding one another from the nuclear

charge, whereas electrons in filled inner shells are highly effective at shielding electrons in outer shells from


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the nuclear charge. Thats why atomic radii on the left of the table are larger their innermost orbitals are

all filled, effectively neutralizing a large portion of the nuclear charge. This leaves the outermost orbitals

with closer to 1. However, as Zincreases, on the outermost orbitals also increases, because newelectrons added to the outermost shells dont effectively neutralize the increasing nuclear charge. Thus,

atomic radii decrease from left to right across a row and increase from top to bottom within a column.

IONIC RADII AND ISOELECTRONIC SERIES

A cation (+ charge) is always smaller than its parentneutral atom due to fewer electrons being subjected to the

same nuclear charge. The more positive the charge of the same

element, the smaller it is.

An anion ( charge) is always larger than its parentneutral atom due to more electrons being subjected to the

same nuclear charge. The more negative the charge of the sameelement, the bigger it is.


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ELECTRON AFFINITY

The electron affinity (EA) of an element E is defined as the energy change that occurs when an electron is

added to a gaseous atom:

Unlike ionization energies, which are always positive for a neutral atom because energy is required to

remove an electron, electron affinities can be negative (energy is released when an electron is added),

positive (energy must be added to the system to produce an anion) or zero (the process is energetically

neutral). The secondelectron affinity is always positive because the increased electron-electron repulsions

in a dianion are far greater than the attraction of the nucleus for the extra electrons.


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