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, 45-54, 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.

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

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 ↑

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

Transition between Classical and Quantum Theory Max Planck (1900); Blackbody Radiation

– 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

– Photoelectric Effect: Light shining on a clean metal

_→

electrons are only emitted when

the light they absorb has a minimum threshold frequency, ν0.

– For ν < ν0

→

no electrons are emitted

– For ν > ν0

→

electrons are emitted, more e

– _{emitted with greater intensity of light,}

– Einstein applied Planck's quantum theory to light.

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).

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".

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 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

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.

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.

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 (ψ2) 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

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 the probability map for the 1s orbital, where the darker regions indicate where the electron is more likely to be found.

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.

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.

d orbitals: – 5 types: dyz, dxz,dxy ,d_x2 _y2 ,d_z2

−

– 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.

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] = 1s2

[Ne] = 1s2 2s2 2p6

[Ar] = 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 Core Notation:

a. Electron configuration for Fe using full notation: 1s2 2s2 2p6 3s2 3p6 4s2 3d6 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)

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

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: phosphorus: oxygen: fluorine:

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+

S S2–

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 S}2– _{is isoelectronic with _______.}

Ex. 1: Circle all of the following ions that are isoelectronic with argon:

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:

Ion

Isoelectronic with what element?

Electron Config.

using core notation Ion

Isoelectronic with what

element?

Electron Config. using core notation

Na+ I–

P–3 Se–2

Al+3 _Ti+4

11.11 ATOMIC PROPERTIES AND THE PERIODIC TABLE

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 b. Na or Al c. In or I

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 upside- down 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.

_________ < _________ <_________ < _________ <_________