Download chapter 11: modern atomic theory

CHAPTER 11: MODERN ATOMIC THEORY
Active Learning Questions: 1-2, 8-10, 14-18; End-of-Chapter Problems: 3-9, 11-13, 16, 18, 20-36, 45-52, 56-64,
66b, 67, 69-91, 98, 101-102, 108, 110, 113, 116,
11.2 ELECTROMAGNETIC RADIATION
Light is a form of electromagnetic radiation, a type of energy that travels through space at a
constant speed, known as the speed of light (symbol c): 2.998×108 m/s (~186,000 mi./hour)
– While light may appear instantaneous to us, it is really a wave traveling at this finite speed.
The term electromagnetic comes from the theory
proposed by Scottish scientist James Clerk Maxwell
that radiant energy consists of waves with an
oscillating electric field and an oscillating
magnetic field, which are perpendicular to one
another.
NASA’s Tour of the Electromagnetic Spectrum video
https://www.youtube.com/watch?v=HPcAWNlVl-8
Electromagnetic Spectrum: continuum of radiant energy (see Fig. 11.4 on p. 240)
– The substances below are about the size of the wavelength indicated in the EM spectrum.
– e.g., an atom is about 10-10-10-9 m in size while a CD is about 10-3 m (or 1 mm) thick.
visible region: the portion of the EM spectrum that we can perceive as color
For example, a "red-hot" or "white-hot" iron bar freshly removed from a high-temperature
source has forms of energy in different parts of the EM spectrum
– The red or white glow falls within the visible region, and heat falls within the infrared region.
CHEM 139: Zumdahl Chapter 11 page 1 of 17 Thus, these electromagnetic waves have both a wavelength and a frequency:
wavelength (λ=Greek “lambda”): distance between successive peaks
frequency (ν=Greek “nu”): number of waves passing a given point in 1 s
How is energy related to wavelength and frequency?
– As the wavelength ↑, the frequency ↓, and the energy ↓
– As the wavelength ↓, the frequency ↑, and the energy ↑
Example: Circle one for each of the examples below:
a. Which has higher frequency?
red light at 700 nm
blue light at 400 nm
b. Which has higher energy?
red light at 700 nm
blue light at 400 nm
CHEM 139: Zumdahl Chapter 11 page 2 of 17 Classical Descriptions of Matter
John Dalton (1803)
– Atoms are hard, indivisible, billiard-like particles.
– Atoms have distinct masses (what distinguishes on type of atom from another).
– All atoms of an element are the same.
JJ Thomson (1890s)
– discovered charge-to-mass ratio of electrons
→ atoms are divisible because the electrons are one part of atom
Ernest Rutherford (1910)
– shot positively charged alpha particles at a thin foil of gold
→ discovery of the atomic nucleus
James Maxwell (1873)
– visible light consists of electromagnetic waves
How Stuff Works: Classical Gas video: https://www.youtube.com/watch?v=yXsHflXB7QM
Transition between Classical and Quantum Theory
Max Planck (1900); Blackbody Radiation: https://www.youtube.com/watch?v=AjnBGWLAoZY
– heated solids to red or white heat
– noted matter did not emit energy in continuous bursts, but in whole-number multiples of
certain well-defined quantities
→ matter absorbs/emits energy in bundles = "quanta"
(single bundle of energy= "quantum")
Albert Einstein (1905); Photoelectric Effect: https://phet.colorado.edu/en/simulation/photoelectric
– Photoelectric Effect: Light shining on a clean metal → electrons are only emitted when
the light they absorb has a minimum threshold frequency, ν .
0
– For ν < ν → no electrons are emitted
0
– For ν > ν → electrons are emitted, more e– emitted with greater intensity of light,
– Einstein applied Planck's quantum theory to light.
→ Light exists as a stream of "particles" called photons.
0
CHEM 139: Zumdahl Chapter 11 page 3 of 17 11.3
EMISSION OF ENERGY BY ATOMS
The color display of fireworks results from atoms absorbing energy and becoming excited.
Source: http://en.wikipedia.org/wiki/Fireworks However, atoms in an excited state are higher in energy and unstable.
→ When they return to a lower, more stable energy state, they release photons (or light
energy), sometimes in the form of visible light that we can observe as colored light.
– Different elements give off different energy, which leads to their characteristics colors
(e.g. calcium for orange, barium and copper for green, lithium for reddish-pink, etc.).
– The color depend on the arrangement of electrons within each element since elements
differ in the numbers of protons and electrons.
→ Elements that emit visible colors emit unique colors (see flame tests below).
Flame tests of barium, lithium, calcium, sodium, copper, and potassium. CHEM 139: Zumdahl Chapter 11 page 4 of 17 11.4
THE ENERGY LEVELS OF HYDROGEN
Emission Spectra: continuous or line spectra of radiation emitted by substances
– a heated solid (e.g. the filament in an incandescent light bulb) emits light that spreads out
to give a continuous spectrum = spectrum of all wavelengths of light, like a rainbow
Hydrogen Line Spectrum
– In contrast, when a sample of hydrogen is electrified, the resulting hydrogen emission
spectrum contains only a few discrete lines:
These discrete lines correspond to specific wavelengths → specific energies
→ The hydrogen atoms’ electrons can only emit certain energies
→ The energy of the electrons in the atom must also be quantized.
→ Planck’s postulate that energy is quantized also applies to the electrons in an atom.
– Each element has a unique line spectrum.
→ Emission spectra can be used to identify unknown elements in chemical analysis.
→ The element’s line spectrum is often called its "atomic fingerprint".
– Line spectra can also be used to determine the elements present in suns/stars.
CHEM 139: Zumdahl Chapter 11 page 5 of 17 11.5
THE BOHR MODEL OF THE ATOM
A Danish physicist named Niels Bohr used the results from the hydrogen emission spectrum
to develop a quantum model for the hydrogen atom.
Bohr Postulates: Bohr Model of the Atom: https://phet.colorado.edu/en/simulation/discharge-lamps
1. Energy-level Postulate
– Electrons move in discrete (quantized), circular orbits around the nucleus, just like
planets orbit around the sun.
– "Ball and Stairs" analogy for electrons and energy levels
– A ball can bounce up to or drop from one stair to another, but it can never sit
halfway between two levels.
– Each orbit has a specific energy associated with it, indicated as the principal energy
level or quantum number, n=1, 2, 3,...
– ground state or ground level (n = 1): lowest energy state for atom
– when the electron is in lowest energy orbit in hydrogen
– excited state: when the electron is in a higher energy orbit (n = 2,3,4,...)
2. Transitions Between Energy Levels
– When an atom absorbs energy
→ the electron can jump from a lower energy orbit to a higher energy orbit.
– When an electron drops from a higher energy level to a lower energy level
→ the atom releases energy, sometimes in the form of visible light.
CHEM 139: Zumdahl Chapter 11 page 6 of 17 11.6 THE WAVE MECHANICAL MODEL OF THE ATOM
Limitations of the Bohr Model → Quantum Mechanical Model
– Unfortunately, the Bohr Model only works for the hydrogen atom and single-electron
systems (i.e., charged particles that only have a single electron).
– It fails to predict the spectra for all other elements that have more than one electron.
(The multiple electron-nuclear attractions, electron-electron repulsions, and nuclear
repulsions make other atoms much more complicated than hydrogen.)
Quantum Mechanical Model
In the 1920s, a new discipline, quantum mechanics, was developed to describe the motion of
submicroscopic particles confined to tiny regions of space.
– Quantum mechanics makes no attempt to specify the position of a submicroscopic particle
at a given instant or how the particle got there.
– It only gives the probability of finding submicroscopic particles (e.g. food court analogy).
→ Rather than predicting how the electron moves, we can only predict the probability of
finding the electron in a given region around the nucleus. (See Fig. 11.19 on p. 248).
→ View “Bizarre Quantum Mechanics Explained…” animation
Dual Nature of the Electron
Louis de Broglie (1924)
– If light can behave like a wave and a particle
→ Matter (like an electron) can behave like a wave.
– The smaller a particle, the greater its wave properties.
– Wave properties are insignificant for large objects like a baseball.
→ If we throw a baseball, we can predict where it will land given its mass, velocity, etc.
– Wave properties are significant for very small particles like an electron.
→ We cannot predict the motion of subatomic particles like an electron.
CHEM 139: Zumdahl Chapter 11 page 7 of 17 Werner Heisenberg (1927); Heisenberg Uncertainty Principle
– For very small particles (e.g. proton, neutrons, electrons), there is an inherent uncertainty
in the particles’ position and motion.
→ It is impossible to determine both the particle’s position and its momentum.
→ It is impossible to determine the position and momentum of an electron as it moves
around a nucleus.
11.7
THE HYDROGEN ORBITALS
However, every wave has a specific frequency and energy.
→ The general location occupied by an electron within an atom can be predicted.
Whereas the hydrogen atom only has energy levels that are numbered (e.g. 1, 2, 3, etc.),
atoms with more than one electron have much more complicated energy levels.
→ These energy levels are divided into principal energy levels, and each principal energy
level is further subdivided into sublevels designated by different letters.
Principal Energy Level (n=1, 2, 3,…):
– Indicates the size and energy of the orbital occupied by the electron
– As n increases, the orbital becomes larger, so the electron spends more time further
away from the nucleus.
→ The further the electron is from the nucleus, the higher its energy.
Principal energy levels split into energy sublevels: s, p, d, f sublevels
Energy Levels and Sublevels
– For all other elements (with more than 1 proton and more than 1 electron), principal
energy levels (numbered 1, 2, 3,…) are further divided into energy sublevels.
principal energy level (or
shell), n: n=1,2,3,...
energy sublevels: s, p, d, and f
(or subshells)
These sublevels consist of
orbitals with specific shapes
corresponding to the probability
of finding the electron in a given
region in space.
→ An electron within a given energy sublevel doesn't orbit around the nucleus.
→ Instead, it has a high probability of being found within a given volume corresponding to
the orbital and its energy.
CHEM 139: Zumdahl Chapter 11 page 8 of 17 ORBITALS AND THEIR SHAPES
Erwin Schrödinger (1926)
– developed a differential equation to find the electron's wave function (ψ), and the square
of the wave function (ψ ) indicates the probability of finding the electron near a given point
– probability density for an electron is called the "electron cloud"
→ “shape” of atomic orbitals
2
For example, for the hydrogen 1s orbital, the size of the orbital is defined by the sphere
that contains 90% of the total electron probability.
This is a boundary
surface representation
of the 1s orbital,
indicating the overall
volume and shape of
the orbital occupied by
the electrons in the
orbital.
This is the probability
map for the 1s orbital,
where the darker
regions indicate where
the electron is more
likely to be found.
s orbitals: spherical
– The size of the orbitals increase with principal quantum number, n.
→ 1s < 2s < 3s, etc.
p orbitals: dumbbell-shaped
– 3 types: px, py, pz (where x, y, and z indicates axis on which orbital aligns)
– The figures below shows the probability maps and the boundary surface
representations of the p orbitals, px, pz, and py.
CHEM 139: Zumdahl Chapter 11 page 9 of 17 d orbitals:
– 5 types: dyz, dxz, dxy , d x 2 −y 2 , dz2
– These figures show the boundary surface representations of the d orbitals.
11.9 ELECTRON ARRANGEMENTS IN THE FIRST 18 ATOMS ON THE PERIODIC TABLE
electron configuration: shorthand description of the arrangement of electrons within an atom
REMEMBER that each orbital can only hold 2 electrons!
– each s orbital can hold 2 electrons
– a set of p orbitals can hold 6 electrons
– a set of d orbitals can hold 10 electrons
– a set of f orbitals can hold 14 electrons
Writing Electron Configurations
1. Electrons are distributed in orbitals of increasing energy levels.
2. Once an orbital has the maximum number of electrons it can hold, it is considered “filled.”
Remaining electrons must then be placed into the next highest energy orbital, and so on.
– Consider the parking garage analogy.
Orbitals in order of increasing energy:
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 5d < 6p
Ex. 1 He →
_____ e
electron configuration for He: _____________________
Ex. 2 C →
_____ e
C: _______________________________________
Ex. 3 S →
_____ e
S: _______________________________________
Ex. 4 K →
_____ e
K: _______________________________________
Ex. 5 Fe → _____ e
Fe: _______________________________________
−
−
−
−
−
These are called ground state electron configurations since they represent the most stable
form of an atom in which all of its electrons are in the lowest energy levels.
– When an atom gains energy, its electrons can be excited to higher energy levels.
→ In an excited state electron configuration, some lower energy levels are not filled.
CHEM 139: Zumdahl Chapter 11 page 10 of 17 11.10 ELECTRON CONFIGURATIONS AND THE PERIODIC TABLE
Blocks of Elements
The shape of the Periodic Table actually corresponds to the order of energy sublevels.
– Consider the figure below to see how electrons for each element are distributed into energy
sublevels.
Electron configurations of atoms with many electrons can become cumbersome.
→ Core notation using Noble gas configurations:
– Elements in the last column of the Periodic Table are called “noble gases.”
– Since noble gases are at the end of each row in the Periodic Table, all of their electrons
are in filled orbitals.
[He]
[Ne]
[Ar]
= 1s2
= 1s2 2s2 2p6
= 1s2 2s2 2p6 3s2 3p6
– Such electrons are called “core electrons” since they are more stable (less reactive)
when they belong to completely filled orbitals.
→ Noble gas electron configurations can be used to abbreviate the “core electrons” of all
elements
→ Electron configurations using Noble gas abbreviations are called “core notation”
CHEM 139: Zumdahl Chapter 11 page 11 of 17 Electron Configurations using Core Notation:
1s2 2s2 2p6 3s2 3p6 4s2 3d6
a. Electron configuration for Fe using full notation:
Electron configuration for Fe using core notation: [Ar] 4s2 3d6
b. Electron configuration for Cl using full notation: ________________________________
Electron configuration for Cl using core notation: ________________________________
c. Electron configuration for Ni using full notation: ________________________________
Electron configuration for Ni using core notation: ________________________________
d. Electron configuration for Sr using core notation: ________________________________
e. Electron configuration for Mg using core notation: ________________________________
f. Electron configuration for Se using core notation: ________________________________
g. Electron configuration for I using core notation: ________________________________
Exceptions to the Building-Up Principle (for Cr, Mo, W, Cu, and Ag)
Atoms gain extra stability with half-filled or completely filled d subshells.
→ If we can fill or half-fill a d subshell by promoting an electron from an s orbital to a d orbital,
we do so to gain the extra stability.
Example: Write the electron configurations for the following using Noble Gas core notation:
Transition Metal
expected electron configuration
actual electron configuration
copper
molybdenum (Mo)
silver
chromium
tungsten (W)
Note: Be able to write ground state electron configurations for elements #1-56.
CHEM 139: Zumdahl Chapter 11 page 12 of 17 VALENCE ELECTRONS
core electrons: innermost electrons belonging to filled electron shells
valence electrons: Electrons in the outermost shell
– Since atoms want filled electron shells to be most stable, they’ll combine with other atoms
with unfilled shells (gaining or losing e–s) to get stability.
→ Valence electrons lead to chemical bonds and reactions between atoms.
→ An element’s chemical properties are determined by its number of valence electrons.
Ex. 1: Use core notation to write the electron configuration for chlorine: _______________
Ex. 2: A neutral chlorine atom has _____ core electrons and _____ valence electrons.
For Main Group (A) elements, Group # → # of valence electrons
– Elements in Group IA: Each has 1 valence electron
– Elements in Group IIA: Each has 2 valence electrons
– Elements in Group IIIA: Each has 3 valence electrons
– Elements in Group IVA: Each has 4 valence electrons
– Elements in Group VA: Each has 5 valence electrons
– Elements in Group VIA: Each has 6 valence electrons
– Elements in Group VIIA: Each has 7 valence electrons
– Elements in Group VIIIA: Each has 8 valence electrons
argon
Electron-Dot (or Lewis) Symbols
– Show the atom of an element with
1. Element symbol representing the nucleus and core electrons
2. Dots representing the valence e–
Rules for writing Electron Dot Symbol
1. Write down the element symbol
2. Determine the number of valence electrons using the group number
3. Assume the atom has four sides, and distribute electrons with one electron per side
before pairing electrons.
Write the Lewis symbol for each of the following:
boron:
CHEM 139: Zumdahl Chapter 11 phosphorus:
oxygen:
fluorine:
page 13 of 17 12.4 STABLE ELECTRON CONFIGURATIONS AND CHARGES ON IONS
Although we do not delve into the quantitative aspects of the quantum-mechanical model in
this course, calculations show that atoms and ions that have the same number of valence
electrons as the noble gases (2 valence electrons for helium and 8 valence electrons for all
the other noble gases) are very low in energy and are therefore stable.
Thus, elements tends to gain or lose electrons, so they are isoelectronic with (have the same
number of electrons as) a Noble gas to become more stable.
Ex. 1: Indicate the number of protons and electrons for the following:
Na+
Na
S2–
S
Ex. 2: Given that metals generally lose electrons and nonmetals generally gain electrons,
write the formula for the ion formed by each of the following elements:
calcium: _______
nitrogen: _______
phosphorus: _______
oxygen: _______
chlorine: _______
magnesium: _______
barium: _______
fluorine: _______
potassium: _______
isoelectronic: has the same number of electrons
Thus, Na+ is isoelectronic with _______, and S2– is isoelectronic with _______.
Ex. 1: Circle all of the following ions that are isoelectronic with argon:
K+
Sr2+
CHEM 139: Zumdahl Chapter 11 Al3+
P3
Ti4+
−
Ca2+
O2
−
Mg2+
page 14 of 17 Electron Configurations of Cations and Anions
For IONS, one must account for the loss or gain of electrons:
# electrons = atomic # – (charge = change in # of valence electrons)
Or you can simply use the Periodic Table
– Find out with which element the ion is isoelectronic
– Move to the left for electrons lost or to the right for electrons gained
→ write the electron configuration for that element
Example 1: Fill in the blanks for the following ions:
Isoelectronic
Electron Config.
Ion
with what
Ion
using core notation
element?
Na+
I–
P–3
Se–2
Al+3
Ti+4
Isoelectronic
with what
element?
Electron Config.
using core notation
11.11 ATOMIC PROPERTIES AND THE PERIODIC TABLE
Atomic Radius: distance from the nucleus to the outermost electrons
CHEM 139: Zumdahl Chapter 11 page 15 of 17 Periodic Trend for Atomic Radius
– Increases down a group: More p+, n, and e–
→ bigger radius
– Decreases from left to right along a period:
– Effective nuclear charge: # of protons – # of core electrons
– Number of p+ and e– increases, but electrons going into same orbitals.
– The higher the effective nuclear charge → smaller radius because nucleus pulling e– in
Example: Compare an Al atom with a Cl atom below:
Trend from top to bottom → like a snowman
Trend from left to right → like a snowman
that fell to the right
Metallic Character: Tendency to behave like a metal rather than a nonmetal
Periodic Trend for Metallic Character:
– Decreases from left to right along a period:
Metals are concentrated on the left-hand side of P.T.; nonmetals are on the right-hand side.
– Increases down a group: Looking at groups IVA and VA, go from nonmetals (C & N) to
semimetals (Si & As) to metals (Sn & Bi).
→ Same snowman trends as for atomic radius!
Ex. 1: Circle the element in each pair below with the greater metallic character:
a.
Na
or
Cs
CHEM 139: Zumdahl Chapter 11 b.
Na
or
Al
c.
In
or
I
page 16 of 17 IONIZATION ENERGY (I.E.): Energy required to remove an electron from a neutral gaseous
atom to make it an ion.
Na(g) + ionization energy
Na+(g)
→
+
e–
Periodic Trend for Ionization Energy
– Decreases down a group:
The bigger the atom, the farther away the electrons are from the protons in the nucleus.
→ The electrons are held less tightly and are more easily removed.
– Increases from left to right along a period:
– Elements with fewer (1–3) valence electrons can more easily give up electrons to
gain noble gas configuration (stability)
– Elements with more (4–7) valence electrons can more easily gain electrons to gain
noble gas configuration (stability)
Trend from top to bottom → like an upsidedown snowman
Trend from left to right → like a upside-down
snowman that fell to the right
Ex. 1: Rank the following elements in terms of increasing atomic radius:
sulfur, fluorine, oxygen, calcium , potassium.
_________ < _________ <_________ < _________ <_________
smallest radius
largest radius
Ex. 2: Rank the following elements in terms of increasing ionization energy:
sulfur, fluorine, oxygen, calcium , potassium.
_________ < _________ <_________ < _________ <_________
smallest I.E.
CHEM 139: Zumdahl Chapter 11 largest I.E.
page 17 of 17