Download Chapter 7 Atomic Structure and Periodicity

Dheemanth Manjunath
Period 6 04/10/06
Mrs. Barbara Young AP Chemistry
D_shorty’s Quickster’s Guide on Chemistry Zumdahl Fifth Edition Textbook: Chapter 7
Chapter 7 Atomic Structure and Periodicity
7-1 Electromagnetic Radiation
-Electromagentic Radiation – light.
-Waves have three primary characteristics: Wavelength, frequency, and speed.
-Wavelength – (symbolized by the Greek letter lambda, λ) is the distance between two consecutive peaks or troughs
in a wave.
-Frequency – (symbolized by the Greek letter nu, ν) is defined as the number of waves (cycles) per second that pass
a given point in space.
-Short – wavelength radiation must have high frequency.
-An inverse relationship between wavelength and frequency exists, that is, λ = 1/ν or
λν=c
where λ is the wavelength in meters, ν is the frequency in cycles per second, and c is the speed of light (2.9979 
108 m/s). In the SI system, cycles are understood, and the unit per second becomes 1/s, or s -1, which is called the
hertz (abbreviated Hz).
7-2 The Nature of Matter
-German physicist Max Planck (1858-1947) could account for his observations only by postulating that energy can
be gained or lost only in whole-number multiples of the quantity hν, where h is a constant called Planck’s constant,
determined by experiment to have the value 6.626 x 10 -34 J  s. That is, the change in energy for a system ΔE can be
represented by the equation:
ΔE = nhν
Where n is an integer (1, 2, 3, …), h is Planck’s constant, and ν is the frequency of the electromagnetic radiation
absorbed or emitted.
-Quantized – Energy can occur in discrete units of the size hν.
-Quantum – “Small packets” of energy.
-A system can transfer energy only in whole quanta.
-Photons – Electromagnetic radiation that can be viewed as a stream of “particles.”
-The energy of each photon is given by the expression:
Ephoton = hν = hc/λ
where h is Planck’s constant, ν is the frequency of radiation, and λ is the wavelength of radiation.
-In a related development, Einstein derived the famous equation: E = mc 2.
The main significance of this equation is that energy has mass:
m = E/c2
2
where m is the mass, E is the energy, and c is the speed of light.
-Using this form of the equation, we can calculate the mass associated with a given quantity of energy. For
example, we can calculate the apparent mass of a photon. For electromagnetic radiation of wavelength λ, the energy
of each photon is given by the expression:
Ephoton = hc/λ
Then the apparent mass of a photon of light with wavelength λ is given by:
m = E/c2 = hc/λ/c2 = h/λc
-Summary of Einstein’s and Planck’s work:
a) Energy is quantized. It can occur in only discrete units called quanta.
b) Electromagnetic radiation, which was previously thought to exhibit only wave properties, seems to show
certain characteristics of particulate matter as well. This phenomenon is sometimes referred to as the dual
nature of light.
-Recall that the relationship between mass and wavelength for EMR is m = h/λc. For a particle with velocity ν, the
corresponding expression is:
m = h/λν
Rearranging to solve for λ, we have:
λ = h/mν
This equation, called de Broglie’s equation, allows us to calculate the wavelength for a particle.
-Diffraction – When light is scattered from a regular array of points or lines.
-Diffraction Pattern – Pattern of bright spots and dark areas on a photographic plate.
-All matter exhibits both particulate and wave properties.
7-3 The Atomic Spectrum of Hydrogen
-Continuous Spectrum – Results when white light is passed through a prism, which contains all the wavelengths of
visible light.
-Line Spectrum – The hydrogen emission spectrum.
-Line spectrum of hydrogen indicates that only certain energies are allowed for the electron in the hydrogen atom.
-A given change in energy from a high to a lower level would give a wavelength of light that can be calculated from
Planck’s equation:
ΔE = hν = hc/λ
where ΔE is the change in energy, hν is the frequency of the light that is emitted, and λ is the wavelength of light
emitted.
7-4 The Bohr Model
-Quantum Model – Electron in a hydrogen atom moves around the nucleus only in certain allowed orbits.
-Correct model had to account for the experimental spectrum of hydrogen, which showed that only certain electron
energies were allowed.
-Energy levels available to the electron in the hydrogen atom:
E = -2.178  10-18 J (z2/n2)
(7.1)
in which n is an integer (the larger value of n, the larger is the orbit radius) and x is the nuclear charge.
-The negative sign in equation (7.1) simply means that the energy of the electron bound to the nucleus is lower than
it would be if the electron were at an infinite distance (n = ) from the nucleus, where there is no interaction and the
energy is zero:
E = -2.178  10-18 J (z2/) = 0
-Ground State – Lowest possible energy state for an atom.
-ΔE = Energy of final state – Energy of initial state
-The wavelength of the emitted photon can be calculated from the equation:
ΔE = h(c/λ) or λ = hc/ΔE
-At this time we must emphasize two important points about the Bohr model:
1) The model correctly fits the quantized energy levels of the hydrogen atom and postulates only certain
allowed circular orbits for the electron.
2) As the electron becomes more tightly bound, its energy becomes more negative relative to the zero-energy
reference state (corresponding to the electron being at infinite distance from the nucleus). As the electron
is brought closer to the nucleus, energy is released from the system.
-Using equation (7.1), we can derive a general equation for the electron moving from one level (n initial) to another
level (nfinal):
ΔE = Energy of level nfinal – Energy of level ninitial
= Efinal - Eintial
= (-2.178  10-18 J)(12/nfinal2) – (-2.178  10-18 J)(12/ninitial2)
= -2.178  10-18 J (1/nfinal2 - 1/ninitial2)
7-5 The Quantum Mechanical Model of the Atom
-Werner Heisenberg (1901-1976), Louis de Broglie (1892-1987), and Erwin Schroedinger (1887-1987); quantum
mechanics.
-Standing Wave – Seemed similar to electrons bound to the nucleus.
-Schroedinger’s Equation:
Ĥ = E
where  called the wave function, is a function of the coordinates (x, y, and z) of the electron’s position in three
dimensional space and Ĥ represents a set of mathematical instructions called an operator. In this case, the operator
contains mathematical terms that produce the total energy of the atom when they are applied to the wave function. E
represents the total energy of the atom (the sum of the potential energy due to the attraction between the proton and
electron and the kinetic energy of the moving electron). When thus function is analyzed, many solutions are found.
Each solution consists of a wave function  that is characterized by a particular value of E.
-Orbital – Specific wave function.
-There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle
at a given time. Known as the Heisenberg Uncertainty Principle.
-Stated mathematically: Δx  Δ(mv)  h/4
where Δx is the uncertainty in a particle’s position, Δ(mv) is the uncertainty in a particle’s momentum, and h is
Planck’s constant.
-The square of the function indicates the probability of finding an electron near a particular point in space:
[ (x1, y1, z1)]2/[ (x2, y2, z2)]2 = N1/N2
The quotient N1/N2 is the ratio of the probabilities of finding the electron in positions 1 and 2.
-Probability Distribution – In which the intensity of color is used to indicate the probability.
-Radial Probability Distribution – When the total probability of finding the electron in each spherical shell is
plotted versus the distance from the nucleus.
-The definition most often used by chemists to describe the size of the hydrogen 1s orbital is the radius of the sphere
that encloses 90 of the total electron probability.
7-6 Quantum Numbers
-Quantum Numbers – Characterized by a series of numbers, which describe various properties of the orbital.
-Principal Quantum Number – (n) has integral values 1, 2, 3 . . . The principal quantum number is related to the
size and energy of the orbital. As n increases, the orbital becomes larger and the electron spends more time further
form the nucleus. An increase in n also means higher energy, because the electron is less tightly bound to the
nucleus, and the energy is less negative.
-Angular Momentum Quantum Number – (cursive L) has integral values from 0 to n-1 for each value of n. This
quantum number is related to the shape of the atomic orbitals. The value of (cursive L) for a particular orbital is
commonly assigned a letter: (cursive L) = 0 is called s; (cursive L) = 1 is called p; (cursive L) = 2 is called d;
(cursive L) = 3 is called f.
-Magnetic Quantum Number – (mcursive L) has integral values between (cursive L) and –(cursive L), including zero.
The value of (mcursive L) is related to the orientation of the orbital in space relative to the other orbitals in the atom.
-Subshell – Set of orbitals with a given value (cursive L).
7-7 Orbital Shapes and Energies
-Nodal Surfaces (nodes) – Areas of high probability separated by areas of zero probability.
-Degenerate – All orbitals with the same value of n have the same energy.
-A summary of the hydrogen atom:
a) In the quantum (wave) mechanical model, the electron is viewed as a standing wave. This representation
leads to a series of wave functions (orbitals) that describe the possible energies and spatial distributions
available to the electron.
b) In agreement with the Heisenberg Uncertainty Principle, the model cannot specify the detailed electron
motions. Instead, the square of the wave function represents the probability distribution of the electron in
that orbital. This allows us to picture orbitals in terms of probability distributions, or electron density
maps.
c) The size of an orbital is arbitrarily defined ad the surface that contains 90 of the total electron probability.
d) The hydrogen atom has many types of orbitals. In the ground state, the single electron resided in the 1s
orbital. The electron can be excited to higher energy orbitals if energy is put into the atom.
7-8 Electron Spin and The Pauli Principle
-Electron Spin – Spin of an electron creating a magnetic charge.
-Electron Spin Quantum Number – (ms) can only have one of two values, +½ or -½.
-Pauli’s Exclusion Principle – In a given atom, no two electrons can have the same set of four quantum numbers
(n, cursive L, mcursive L, and ms).
-Since electrons in the same orbital have the same values of n, cursive L, and mcursive L, this postulate says that they
must have different values of ms. Then, since only two values of ms are allowed, an orbital can only hold two
electrons, and they must have opposite spins.
7-9 Polyelectronic Atoms
-Polyelectronic Atoms – Atoms with more than one electron.
-Electron Correlation Problem – The difficulty arises in dealing with the repulsions between the electrons. Since
the electron pathways are unknown, the electron repulsions cannot be calculated exactly.
-Most commonly, the approximation used to treat each electron as if it were moving in a field of charge that is the
net result of the nuclear attraction and the average repulsions of all the other electrons.
-For a given principal quantum level the orbitals vary in energy as follows:
Ens < Enp < End < Enf
7-10 History of the Periodic Table
-First chemist to recognize patterns; Johann Dobreiner (1780-1849); found several triads (his name for them) in
which three elements had similar chemical properties. His view was severely limited.
-Next notable chemist John Newlands, who in 1864 suggested that elements should be arranged in octaves.
Successful to some extent, but had many discrepancies.
-Present form of the periodic table given credit to Julius Lothar Meyer (1830-1895) and Dmitri Mendeleev (18341907).
-Mendeleev correctly predicted many of the future elements’ masses and atomic numbers.
7-11 The Aufbau Principle and the Periodic Table
-Aufbau Principle – As protons are added one by one to the nucleus to build up the elements, electrons are
similarly added to these hydrogen-like orbitals.
-Hund’s Rule – 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.
-To avoid writing the inner-level electrons, this configuration is often abbreviated as [Ne]3s1, where [Ne] represents
the electron configuration of Neon, 1s2 2s2 2p6.
Configuration: Na: 1s2 2s2 2p6 3s1.
-Valence Electrons – The electrons in the outermost principal quantum level of an atom.
-Core Electrons – Inner valence electrons.
-The elements in the same group (vertical column of the periodic table) have the same valence electron
configuration.
-Transition Metals – A series of 10 elements (Scandium through Zinc), whose configurations are obtained by
adding electrons to the five 3d orbitals.
-Chromium: Expected Configuration: [Ar]4s1 3d10
Actual Configuration: [Ar] 4s1 3d5
-Copper: Expected Configuration: [Ar] 4s1 3d10
Actual Configuration: [Ar] 4s2 3d10
-Following Points:
1) The (n+1)s orbitals always fill before the nd orbitals due to the penetration effect.
2) After Lanthanum, which has the configuration [Xe] 6s2 5d1, a group of 14 elements called the lanthanide
series, or the lanthanides, occurs. This series of elements corresponds to the filling of the seven 4f
orbitals. Note that sometimes an electron occupies a 5d orbital instead of a 4f orbital. This occurs because
the energies of the 4f and 5d orbitals are very similar.
3) After Actinium, which has the configuration [Rn] 7s2 6d1, a group of 14 elements called the actinide series,
or the actinides, occurs. This series corresponds to the filling of the seven 5f orbitals. Note that sometimes
one or two electrons occupy the 6d orbitals instead of the 6f orbitals. This is because the 5f and 6d orbitals
have similar energies.
4) The labels for Groups 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A indicate the total number of valence electrons
for the atoms in these groups.
5) The groups labeled 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A are often called the main group, or
representative, elements.
7-12 Periodic Trends in Atomic Properties
-Ionization Energy – Energy required to remove an electron from a gaseous atom or ion. Atom is assumed to be in
the ground state.
-First Ionization Energy – (I1) The energy required to remove the next highest-energy electron of an atom.
-Second Ionization Energy – (I2) The energy required to remove the next highest-energy electron of an atom and so
forth.
-The largest jump in ionization energy by far occurs in going from the third ionization energy (I 3) to the fourth (I4).
This is so because I4 corresponds to removing a core electron, and core electrons are bound much more tightly than
valence electrons.
-Going across a period from left to right, the first ionization energy increases.
-First ionization energy decreases going down a group.
-Electron Affinity – The energy change associated with the addition of an electron to a gaseous atom.
-More negative the energy, the greater is the quantity of energy released.
-A second electron cannot be added to an oxygen atom.
[O-(g) + e- → O2-(g)]
-Electron affinities become more negative in going from left to right across a period.
-When we go down a group, electron affinity should become more positive (less energy is released). Exception:
Group 7A
-Atomic Radii – Size of the atom.
-Covalent Atomic Radii – Distances between atoms in covalent bonds.
-Metallic Radii – Half the distance between atoms in solid metal crystals.
-Atomic radii decrease in going from left to right across a period. This decrease can be explained in terms of the
increasing effective nuclear charge (decreasing shielding) in going from left to right. This means that the valence
electrons are drawn closer to the nucleus, decreasing the size of the atom.
-Atomic radii increases going down a group, because of the increases in the orbital sizes in successive principal
quantum levels.
7-13 The Properties of a Group: The Alkali Metals
-Metalloids (semimetals) – Many elements along the division line that exhibit both metallic and non-metallic
properties under certain circumstances.
-Lithium, Sodium, Potassium, Rubidium, Cesium, and Francium are the most chemically reactive of the metals.
-Although Hydrogen is found in Group 1A of the periodic table, it behaves as a non-metal. The fundamental reason
for Hydrogen’s non-metallic character is its very small size. The electron in the small 1s orbital is bound tightly to
the nucleus.
-The smooth decrease in melting point and boiling point in going down Group 1A is not typical.
-The expected trend in reducing ability is:
Cs > Rb > K > Na > Li
D_shorty’s Quickster’s Quiz
1) Oxygen, which is 16 times as dense as hydrogen, diffuses
a) 1/16 times as fast
b) 1/4 times as fast
c) 4 times as fast
d) 16 times as fast
2) Lead(II) fluoride (PbF2), lead(II) chloride (PbCl2), lead(II)
bromide (PbBr2), and lead(II) iodide (PbI2) are all slightly
soluble in water. Which lead salt will increase in
solubility when its saturated solution is acidified?
a) PbF2
b) PbCl2
c) PbBr2
d) PbI2
3) Which reaction occurs with an increase in entropy?
a) 2C(s) + O2(g) ® 2CO(g)
b) 2H2S(g) + SO2(g) ® 3S(s) + 2H2O(g)
c) 4Fe(s) + 3O2(g) ® 2Fe2O3(s)
d) CO(g) + 2H2(g) ® CH3OH(l)
4) What are the strongest intermolecular force between
neighboring carbon tetrachloride, CCl4, molecules?
a) dipole-dipole forces
b) dispersion forces
c) hydrogen bonds
d) covalent bonds
5) What will happen to the pH of a buffer solution when a
small amount of a strong base is added? The pH will
a) increase slightly
b) decrease slightly
c) remain exactly the same
d) become 7.0
6) What volume of 0.108 M H2SO4 is required to
neutralize 25.0 mL of 0.145 M KOH?
a) 16.8 mL
b) 33.6 mL
c) 37.2 mL
d) 67.1 mL
7) One of the steps in the manufacture of nitric acid is the
oxidation of ammonia shown in this equation.
4NH3(g) + 5O2(g) . 4NO(g) + 6H2O(g)
If gaseous water appears at a rate of 0.025 mol·min–1, at
what rate does ammonia disappear?
a) 0.0040 mol·min–1
b) 0.017 mol·min–1
c) 0.038 mol·min–1
d) 0.150 mol·min–1
8) The reaction A + B ® AB has an enthalpy of reaction of
–85.0 kJ·mol–1. If the activation enthalpy for the forward
reaction is 120.0 kJ·mol–1, what is the activation energy
for the reverse reaction AB ® A + B?
a) 35.0 kJ·mol–1
b) 85.0 kJ·mol–1
c) 120.0 kJ·mol–1
d) 205.0 kJ·mol–1
9) Consider this reaction.
2N2H4(l) + N2O4(l) ® 3N2(g) + 4H2O(g) DH = –1078 kJ
How much energy is released by this reaction during the
formation of 140. g of N2(g)?
a) 1078 kJ
b) 1797 kJ
c) 3234 kJ
d) 5390 kJ
10) What pressure (in atm) will be exerted by a 1.00 g sample
of methane, CH4, in a 4.25 L flask at 115°C?
a) 0.139
b) 0.330
c) 0.467
d) 7.50
Answer Form
1) b) 1/4 times as fast
2) a) PbF2
3) a) 2C(s) + O2(g) ® 2CO(g)
4) b) dispersion forces
5) a) increase slightly
6) a) 16.8 mL
7) b) 0.017 mol·min–1
8) d) 205.0 kJ·mol–1
9) b) 1797 kJ
10) c) 0.467