Download Chapter 7 Atomic Structure and Periodicity Study Guide

Chapter 7 Atomic Structure and Periodicity Study Guide – Enlow
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Electromagnetic Radiation:
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Waves have 3 characteristics:
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(1) wavelength (λ) – distance between 2 consecutive peaks or
troughs in a wave, measured in meters
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(2) frequency (ν)- a number of waves (cycles) per sec that pass a give point in space, measured
in Hertz (which is cycles per sec = 1/sec = sec-1)
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(3) speed – all EM waves travel at the speed of light, c = 3.0 x 108 m/s
Wavelength and frequency are inversely related
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The longer the λ, the lower the ν….. they are related through the formula λ ν = c
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In the spectrum below (from left to right)
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wavelength increases, frequency decreases, energy decreases, speed is constant
Nature of Matter
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Max Planck –physicist who determined that energy is gained or lost by substances only in whole number
multiples of the quantity hν (where h=Planck’s constant = 6.626 x 10-34 J s)
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∆E = nhν, where n is an integer
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This means that energy is quantized and can only occur in discrete units of the size hv.
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Each ‘packet’ of energy is called a quantum, making energy particulated (like matter!)
Einstein – suggested that EM radiation was quantized and could be viewed as a stream of “particles”
called photons
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Ephoton = hv = hc/ λ
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E = mc2 which means that energy has mass and there is a mass defect when energy is released
(especially in nuclear fusion)
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This allows us to calculate the mass of a photon m = E/c 2 = h/ λc
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This is referred to as the dual nature of light (wave and mass like properties)
de Broglie – suggested that particles could also have wave like properties
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λ = h/mv…. This is de Broglie’s equation to calculate the wavelength of a particle
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supported by diffraction patterns of substances (caused by their e-)
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larger objects have very short wavelengths
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all matter exhibits both particle and wave properties
The Atomic Spectrum of Hydrogen
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Give atoms excess energy, they become excited, they release the excess energy in different
wavelengths of light to produce an emission spectrum (energy emitted in the form of a photon)
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Continuous spectrum = result of diffraction of white light, contains all wavelengths of light
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Line spectrum = result of diffraction of emission spectrum to produce only specific lines which
correspond to specific wavelengths
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This indicates that only certain energies are allowed for the e- in the atom (aka the energy of
the e- in the atom is quantized)
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Bright line spectra for Hydrogen
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This supports Planck’s theory and show that energy is quantized (not continuous)!!
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∆E = hν a definite change in E corresponds to a definite wavelength and frequency
The Bohr Model
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Quantum model of H atom – proposed that the e- in a H moves around the nucleus only in certain
allowed circular orbits
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e- attracted to the nucleus allowed for the circular path to continue
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set up energy levels equal to the H atom line spectrum
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e- emit definite wavelengths when it returns to a lower energy state (from an excited state)
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E = -2.178 x 10-18 J ( Z2/n2) where Z= nuclear charge, n = integer correlated to energy level
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The (-) sign means that the energy of an e- close to the nuclear is LOWER than far away!
Calculating energy emission when an e- falls back to ground state:
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Calculate the E of the e- in the outer energy level (using the above equation) ex: E6
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Calculate the E of the e- in the inner energy level (using the above equation) ex: E1
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Calculate the ∆E from E of final energy state – E of initial energy state = E1- E6 = - #
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This (-) value means that the ∆E is lost energy so the e- is in a more stable state
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The E is carried away from the atom in the form of a photon of light with the specific
amount of E calculated above. The wavelength that corresponds show the color.
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λ = hc/∆E
In the diagram below, the Lyman series indicates e- transitions resulting in UV emission lines,
the Balmer Series indicates photon emission lines, and the Paschen series indicates IR emission
lines.
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Finally: Bohr’s model correctly shows quantized energy levels and postulated only certain circular orbits
and stated that as the e- becomes more tightly bound, it’s E becomes more (-) and E is released from
the system...However: only applied to H and no other element, and no circular orbits!
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The Quantum Mechanical Model:
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3 scientists: de Broglie, Heisenberg, Schrodinger attempted to describe the structure of an atom with
the definite energy levels that corresponded to the quanta discovered before.
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Schrodinger knew that the electron must have a wavelike character, therefore, related e- to standing
waves.
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Standing waves do not propagate through space and are fixed at both ends (which correlates to the
thought that the orbits of an e- in an atom has a fix circumference and will only allow a fixed number of
wavelengths)
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Only certain size orbits can contain whole #s of wavelengths of the e- which relates to fixed energy
quanta
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Any overlap of wavelengths would cause destructive interference and collapse on itself
Schrodinger’s Equation to describe e-
HΨ= EΨ
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H = mathematical instructions, Ψ = wave function, E = KE+ PE of atom
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Specific Ψ wave functions are called orbitals! Not orbits like Bohr said!
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We use the word orbital to describe the state of existence of an electron. An orbital is really
no more than a mathematical function describing the standing wave that gives the probability of
the electron manifesting itself at any given location in space. More commonly (and loosely) we
use the word to describe the region of space in which an electron is likely to be found. Each
kind of orbital is characterized by a set of quantum numbers n, l, and m These relate,
respectively, to the average distance of the electron from the nucleus, to the shape of the
orbital, and to its orientation in space.
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Heisenberg Uncertainty Principle
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There is a fundamental limitation to just how precisely we can know both the position and
momentum of a particle at a given time…. We know it is in an orbital, but not exactly all of the
details about the location and behavior of it.
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The more accurately we know a particle’s position, the less accurately we know its momentum
and vis versa
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Mathematic formula
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Small particles are highly unpredictable vs larger particles
∆x ×∆ (mv) > h/ 4 π
∆x = uncertainty in the particle's position
∆ (mv) = uncertainty in the particle's momentum
Physical Meaning of the Wave Function
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The square of the Ψ gives us information on the probability of finding an e- near a particular
point in space… it only gives the likelihood, but e- may not definitely be there (uncertainty pr.)
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Ψ2 = probability distribution = electron density map= shown as a picture, where the most
intensely colored portion is where you will most likely find the e- =
atomic orbital
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These maps do not tell information about: how
e- arrived, where it is going next, or when the e- is in that location
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Radial probability distribution graph – shows
that the probability of finding an e- near the nucleus is high, but only
up to a specific radius (indicated by Bohr’s inner most orbit)
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Quantum Numbers: Describe various properties of the orbital
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Principle Quantum Number (n) – integral values (1,2,3…), related to the size and energy of the orbital,
increase in n means that the e- are farther away from the nucleus and have higher E because less
tightly bound to the nucleus
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Angular Momentum Quantum Number (l) – integral values from 0 to n-1 for each value of n, related to
the shape of the atomic orbtials. l is sometimes called a subshell
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l = 0 … s orbital (there is only 1 s orbital)
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l = 1… p orbital (there are 3 p orbitals)
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l = 2 … d orbital (there are 5 d orbitals)
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l = 3…. f orbital (there are 7 f orbitals)
Magnetic Quantum Number (ml) – integral values between l and –l (including zero), related to the
orientation of the orbital in space
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Spin Quantum Number (ms) +1/2 or -1/2 – describes the spin of the e- (clockwise or counterclockwise)
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*** I remember the order of the quantum numbers as PAMS ***
Orbital Shapes and Energies
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Sizes of Orbitals
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Since an orbital is also defined as the surface that surrounds 90% of the total e- probability,
then we can create a shape to encompass that space.
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Orbitals of the same shape grow larger as the n increases,
(however, they also leave a small “node” where there is zero
probability of finding e-s)
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s orbitals = spherical in shape ( l =0)
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p orbitals = 2 lobes separated by a node at the nucleus, labeled
according to the axis along which the lobe lies (2px, 2py, 2pz)
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occur in levels n=2 or higher (no 1p)
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l=1
d orbitals = 4 of the orbitals have 4 lobes each which are centered in
the plane indicated or the 5th orbit is uniquely shaped to have 2 lobes
with belt (l = 2)
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occur in levels n=3 or greater (no 1d or 2 d)
f orbitals = more complex shape, flower like pattern (l =3)
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occur in levels n=4 and greater
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not involved in most bonding in most compounds
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Energies of orbitals
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For hydrogen - All orbitals with the same value of n have the same energy (termed degenerate
orbitals). This is NOT TRUE for polyelectric atoms
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Es < E p < E d < E f
If energy is put into a e- at ground state , it goes to an excited state at a higher energy level
orbital
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Pauli Exclusion Principle and e- spin
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Since we know that e- spin opposite, we know that they produce two oppositely directed magnetic
moments.
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Pauli Exclusion Principle - In a given atom, no two e- can have the same set of 4 quantum numbers….
Which is where the 4th quantum number comes into play!
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Since e- in the same orbital have all of the same quantum numbers, they must have opposite spins
(different ms values). This means that there are only 2 e- allowed per orbital
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Polyelectric atoms- atoms with more than one e
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3 energy contributions are considered
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KE of the e- as they move freely around the nucleus
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PE of the attraction between the nucleus and the e-
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PE of repulsion between 2e-
e- correlation problem and variation of E in energy levels
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e- pathways are unknown and therefore the repulsive forces are also unknown
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polyelectric atoms experience e- screening or e- shielding from nuclear charge due to repulsions
of other e- (this means that the e- would be more tightly bound if other e- were not present)
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when e- are placed in a particular quantum level, they prefer the lowest energy orbitals first (s
then p then d then f). e- always fill orbitals of the same n in this order!
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This is due to the penetration effect of e- in the s orbital that spend much more time
closer to the nucleus. Due to high attraction between nucleus and e-, the e- in the s
orbitals are of lower energy
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History of the PToE
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Early Scientists= Democritus, Lavoisier, Dalton
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Mendeleev organized his PToE by atomic mass (he used intuition about chemical properties being similar
in groups on the PToE) and the modern PToE is organized by atomic number
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The Aufbau Principle and the PToE
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Aufbau principle describes the pattern in which e- build up the e- configuration in
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It requires the use of all previous principles (Pauli Exclusion – 2 e- with opposite
atoms
spin per orbital)
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Since e- are repulsive, they prefer to fill up orbitals according to Hund’s Rule =
the lowest energy configuration for an atom is the one having the max number of
unpaired e- allowed by the Pauli exclusion principle in a particular set of degenerate orbitals (same
energy orbitals ex: all of the 2p orbitals)
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This means that e- will fill with 1e- per 2p orbital until there are more e- that must go and double up.
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Electron configurations are completed period by period and
all e- are accounted for ex) 1s22s22p4
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Due to the penetration effect, the (n+1)s orbitals
are filled before the nd orbitals
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Sometimes elements in the lanthanide series fill 5d
vs 4f due to energy similarities
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Sometimes elements in the actinide series fill 6d vs
5f due to energy similarities
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Orbital diagrams show the spins of the e- as well as which orbital they are in
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Valence e- can be recognized by the outermost e- in the configuration or
orbital diagram (in outermost principle quantum level, largest n value) –
also indicated by group number of representative elements (not t metals)
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Inner e- are called “core e-“
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Chromium has an exceptional e- configuration
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Copper has an exceptional e- configuration
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[Ar]4s13d5 (both are half filled)
[Ar]4s13d10
PToE Trends: Periodic Law (periodicity) – caused by e- arrangements in
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atoms
Ionization energy (IE) – the energy required to remove an e- from a gaseous atom or ion, where the
gas or ion is assumed to be in its ground state; ex) X(g)  X+ + e- production of a positive ion
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In a stepwise ionization process, it is always the highest energy e- (the one lease tightly bound)
that is removed first.
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The first ionization energy (I1) is the E required to remove the highest energy e-
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The second ionization energy (I2) is the E required to remove the 2nd highest energy e
The 1st is an easy removal compared to the 2nd because the 1st is removed from a neutral
atom and the 2nd is removed from a + charged atom which more tightly binds its e-
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Ex) Al, The 4th ionization is much more difficult because removal of a core e- (not a
valence e-)
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IE increases as we move right on PToE due to the fact that e- added to the same principal
quantum level do not completely shield the increasing nuclear charge caused by adding additional
protons (so e- are more strongly bound as we move right on PToE) (few exceptions due to erepulsion)
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IE decreases as we go down a group because the energy levels are just simply farther from
the nucleus…. Making it easier to remove the e- from outer energy levels
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Electron Affinity (EA)- the energy change associated with the addition of an e- to a gaseous atom
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X(g) + e-  X- (g) production of a negative ion
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The more negative the energy, the greater the quantity of energy released in this exothermic
reaction
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Affinity tends to increase across a period from left to right
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acceptances in each period caused by changes in e- repulsion as e- configs change
(paired e- in p orbitals)
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Affinity tends to decrease down a group (get more positive with less E released) due the outer
energy levels being farther away from the nucleus
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Atomic Radius (AR)- calculated by measurements of distances between atoms (distance /2 = radius)
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Sometimes called covalent atomic radii bc this is how they are measured
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AR decreases going from left to right in a period due to increasing effective
nuclear charge (decreased shielding); valence e- are drawn in closer to nucleus
AR increases going down a group bc there is an increase in orbital size in successive n levels
positive ions are smaller than the atoms from which they are derived
 the greater the size of the + charge, the smaller size of the ion relative to the atom
 negative ions are larger than the atoms from which they are derived
 the greater the size of the - charge, the larger the size of the ion relative to the atom
Properties of a Group on the PToE:
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All groups have the same valence e- configuration which gives all of the elements in that group similar
chemical properties (since it is the valence e- which do all of the reacting!!)
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The most chemically reactive metals are on the lower left portion of the PToE where the IE’s are the
smallest. This means that e- can be removed without much required energy
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Nonmentals are elements with large IEs and the most negative EA (Reactive metals are opposite)\
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Alkali Metals
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Ability to lose valence e-
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Very reactive
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Lower IE
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Make ionic solids
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Behaves as a reducing agent
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Reacts violently with water
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Hydration energy of an ion represents the change in energy that occurs when water moleucles
attach to the metal ion.
Additional Resources:
http://www.chem1.com/acad/webtext/atoms/atpt-6.html#ENC
http://www.chem1.com/acad/webtut/atomic/qprimer/index.html
http://www.chem1.com/acad/webtext/atoms/atpt-1.html#MEU