CHEM 110 - Chapter 3 - Electronic Structure & Periodic Properties of Elements

Electromagnetic radiation

energy that behaves like a wave and travels at the speed of light in a vacuum

Characteristics of Waves

waves have 4 characteristics

• wavelength - the distance between two consecutive peaks in a wave

• frequency - is the number of cycles per second that pass through a point in space

• amplitude - the magnitude of the wave’s displacement

• speed - how fast the wave travels

relating wavelength and frequency

• wavelength and frequency are inversely related

The Ultraviolet Catastrophe

classical electromagnetism did not sufficiently explain empirical observations

Max Planck’s Observations

observed that energy can be gained or lost only in multiples of hv (h: Planck’s constant —> 6.626 × 10^-34 J*s or kg*m²/s)

The Photoelectric Effect

the phenomenon in which electrons are emitted from the surface of a metal when light strikes it

Photons

stream of particles of electromagnetic radiation

• intensity of light is a measure of the number of photons present in the beam

• the energy of photons is directly proportional to the frequency of light

E = mc²

the equation is significant because it shows that energy and mass are related

• the mass associated with a quantity of energy can be calculated

Continuous Spectra

result when white light passes through a prism

• contains all wavelengths of visible light

Line Spectra

displays discrete wavelengths of light

• only certain energies are allowed for the electron in hydrogen atoms

Atomic Spectrum of Hydrogen

when energy is applied to hydrogen gas, hydrogen molecules (H₂) absorb energy and some molecules are split into atoms (H)

• these H atoms are excited

• the excess energy is released in the form of light

Bohr Model for the H-Atom

niels bohr believed that the electrons in hydrogen atoms orbited around the nucleus in certain energy levels

• using assumptions, he calculated the radii for these orbits using classical physics

the bohr model:

• correctly explains emission spectrum of hydrogen (electrons can only exist in certain energy levels, levels are quantized)

• an electron’s energy is related to the energy level it occupies

• if the electron moves further from the nucleus, energy is absorbed

• if the electron moves closer to the nucleus, energy is released

Drawbacks & Insufficiency of the Bohr Model

• the bohr model was insufficient for explaining atoms other than hydrogen

• electrons do not actually move around atomic nuclei in circular orbits

a new approach (quantum mechanics) was developed to explain certain phenomena

The Dual Nature of Light

electromagnetic radiation (and all matter) exhibit properties of both waves and particles

Davisson-Germer Experiment

purpose was to see how electrons scatter & to test Louis de Broglie’s hypothesis that particles like electrons behave like waves

conclusion: electrons did show wave-like behavior

Conventions for Depicting Electrons

by convention:

• the intensity of color indicates the probability value near a given point in space

• the more often an electron occupies a point in space, the darker the space becomes

• these diagrams are called electron density maps

Quantum Numbers

each electron is characterized by a series of quantum numbers

• quantum numbers are used to describe orbitals (the general regions in atoms where electrons are most probable to reside)

The Principal Quantum Number

principal quantum number (n)

• defines the orbital’s size, energy, and distance from the nucleus

• has integer values of 1,2,3…

Angular Momentum Quantum Number

angular momentum quantum number (l)

• specifies shape of the orbital

• has integer values of 0 to n-1 for each value of n

• each value of l is represented by a letter

• (l=0, s) (l=1, p) (l=2, d) (l=3, f) (l=4, g)

Magnetic Quantum Number

magnetic quantum number (ml)

• specifies the orientation of each orbital in 3D space

• informs us regarding the number of each type of orbital per energy level

• has integer values of -l to +l

Nodes

nodes are the areas with zero probability of finding an electron

• the total number of nodes in an orbital is equal to n-1

Electron Spin Quantum Number

electron spin quantum number (ms)

• can have a value of either +1/2 or -1/2

• a 4th quantum number was needed to describe electrons in atoms

• each electron has a magnetic moment with two possible orientations when an atom is placed in a magnetic field

summary:

• n = 1,2,3…

• l = 0,1…(n-1)

• ml = -l,…0,…+l

• ms = +1/2 or -1/2

• (l=0, s) (l=1, p) (l=2, d) (l=3, f) (l=4, g)

The Pauli Exclusion Principle

no two electrons in the same atom can have the same set of 4 quantum numbers, each orbital can hold a maximum of 2 electrons

s orbitals

s orbitals are spherical

• total of 1 s orbitals in any energy level

p orbitals

p orbitals are dumbbell shaped

• labeled according to orientation in 3D space (p_x,y,z)

• total of 3 p orbitals in any energy level

d orbitals

d orbitals have two fundamental shapes

• d_xz, d_yz, d_xy, d_{x^{2 -} z²}, and d_z²

• total of 5 d orbitals in an energy level

Orbital Energies

the energy of atomic orbitals increases:

as n increases (3s orbitals are more energetic than 2s orbitals)

as l increases (3p orbitals are more energetic than 3s orbitals)

Electron Screening (or Shielding)

screening (or shielding) the effect where an electron experiences a reduction in the effective nuclear charge due to electrons occupying inner energy levels

The Penetration Effect

Penetration is the ability of an electron to get close to the nucleus

• Electrons are "penetrating" other shielding electrons

• In the same energy level, penetration power of orbitals: s >p>d >f

• Penetration power decreases as n increases

Degeneracy

Degenerate orbitals are orbitals with the same energy

• In hydrogen, orbitals with the same value for n are degenerate

The Aufbau Principle

The Aufbau principle states that electrons fill the lowest
available energy levels (orbitals) before occupying higher
levels

Hund’s Rule

Hund's rule states:

1) Electrons fill degenerate orbitals singly before pairing

2) Unpaired electrons have the same spin

Rules for Building Orbital Diagrams

1. Identify the total number of electrons to be indicated in the orbital diagram

2. Place electrons in available orbitals with the lowest energy (Aufbau principle)

3. Electrons must occupy all degenerate orbitals before pairing up (Hund's rule)

4. Each orbital can contain a maximum of 2 electrons with opposite spins (Pauli Exclusion principle)

Chemical Behavior & Electronic Structure

elements in the same group exhibit similar chemical behavior

Variation in Atomic Radii

• an atom’s atomic radius is defined as half the distance between the nuclei of two atoms of an element

trends:

• increases down groups

• decreases across periods (left to right)

Variation in Ionic Radii

cations (+ charged ions) are smaller than their parent atoms

• electrons are lost

anions (- charged ions) are larger than their parent atoms

• electrons are gained

Trends in Ionic Radii

isoelectronic ions are ions with the same number of electrons

trends:

• increases down groups

• decreases with effective nuclear charge (for isoelectronic ions)

Variation in Ionization Energies

ionization energy refers to the amount of energy required to remove an electron from an atom or ion

trend:

• decreases down groups

• increases across periods (left to right)

I₁ < I₂ < I_3…

Variation in Electronegativity

electronegativity is the ability of an atom to attract electrons

trends:

• decreases down groups

• increases across periods (left to right)

Dmitri Mendeleev and the Periodic Table

the periodic table was originally organized to represent patterns

mendeleev managed to:

• correct several values for atomic masses

• predict properties of later discovered elements