Atomic Structure and Periodicity By: Lauren Pyfer & Amy Li

CHAPTER 7

CHAPTER CONTENTS

• 7.1 : Electromagnetic Radiation

• 7.2: The Nature of Matter

• 7.3: The Atomic Spectrum of Hydrogen

• 7.4: The Bohr Model

• 7.5: The Quantum Mechanical Model of the Atom

• 7.6: Quantum Numbers

• 7.7: Orbital Shapes and Energies

• 7.8: Electron Spin and Pauli Principal

• 7.9: Polyelectronic Atoms

• 7.10: The History of the Periodic Table

• 7.11: The Aufbau Principal and the Periodic Table

• 7.12: Periodic Trends in Atomic Properties

• 7.13: The Properties of a Group: The Alkali Metals

7.1: ELECTROMAGNETIC RADIATION

• Types of Electromagnetic Radiation

7.1: ELECTROMAGNETIC RADIATION

• Properties of Electromagnetic Waves:Wavelength ( λ ) :

• Distance Between two consecutive peaks or troughs in a wave

• Measured in meters

7.1: ELECTROMAGNETIC RADIATION

• Properties of Electromagnetic Waves: Frequency (ν)

• Number of waves that pass a given point per second

• Measured in Hertz

7.1: ELECTROMAGNETIC RADIATION

• Properties of Electromagnetic Waves: Speed (c)

• Speed of light

• Measured in meters/ second

7.1: ELECTROMAGNETIC RADIATION

• Relationship Between Properties

• Shortest wavelength = highest frequency

• Longest wavelength = lowest frequency

• INVERSE RELATIONSHIP

EXAMPLE PROBLEM: 7.1

• Light with a frequency of 7.26 x 1014 Hz lies in the violet region of the visible spectrum. What is the wavelength of this frequency of light? Answer in units of nm.

answer: 413 nm

7.2 THE NATURE OF MATTER

• Max Plank and Quantum Theory: Energy is gained or lost in whole number multiples of the quantity hv ( frequency = v, Planck’s constant =h)

• Planck’s Constant: h = 6.62606957 × 10-34 m2 kg / s ( J/s)

• Planck discovered that energy is transferred to matter in packets of energy called quantum, rather than energy of matter being continuous.

• Δ E = h ν : T h e q u a n t u m o f e n e r g y c a n b e c a l c u l a te d f r o m t h i s e q u a ti o n

EINSTEIN’S PHOTOELECTRIC EFFECT• Phenomenon in which electrons are emitted from the

surface of a metal when light strikes it

• His observations are explained by assuming electromagnetic radiation is quantized (photons) and the threshold frequency is the minimum energy required to remove the electron.

7.2: THE DUAL NATURE OF MATTER• Dual Nature of Light:

• Light travels through space as a wave

• Light transmits energy as a particle

• Particles have wavelength, exhibited by diffraction patterns

• De Broglie’s Equation: Allows calculation of wavelength for a particle

• λ = h/mv

• Diffraction: results when light is scattered from a regular array of points or lines

• Diffraction Patterns: The interference pattern that results when a wave or a series of waves undergoes diffraction, as when passed through a diffraction grating or the lattices of a crystal. The pattern provides information about the frequency of the wave and the structure of the material causing the diffraction.

7.2: EXAMPLE PROBLEM

What is the wavelength of an electron moving at 5.31 x 106 m/sec?

Given: mass of electron = 9.11 x 10-31 kg

h = 6.626 x 10-34 J·s

Answer: The wavelength of an electron moving 5.31 x 106 m/sec is 1.37 x 10-10 m

7.3: THE ATOMIC STRUCTURE OF HYDROGEN

• Continuous Spectrum: results when white light is passed through a prism. Contains all wavelengths of visible light

• Line Spectrum: only see a few lines, each of which corresponds to discrete wavelength when passed thorough a prism. (Hydrogen emission spectrum)

7.3: EXAMPLE PROBLEM

Calculate the velocity of an electron (mass = 9.10939 x 10¯31 kg) having a de Broglie wavelength of 269.7 pm.

v = 2.697 x 106 m/s

7.4: THE BOHR MODEL

• Quantum Model : electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits

• Bright line spectra confirms that only certain energies exist in the atom, and atom emits photons with definite wavelengths when the electron returns to a lower energy state.

• Energy levels available to the electron in the hydrogen atom: • n= an integer

• z= nuclear charge

• J= energy in Joules

7.4: THE BOHR MODEL

• Calculating the energy of the emitted photon

• Calculate electron energy in outer level

• Calculate electron energy in inner level

• Calculate the change in the energy

• ΔΕ= energy of final state- energy of initial state

• hc/ ΔΕ : to calculate the wavelength of emitted photon

7.4: THE BOHR MODEL

• Energy Change in Hydrogen atoms

• Calculate the energy change between any two energy levels:

7.4 BOHR MODEL

• Limitations of the Bohr Model

• Bohr’s model does not work for atoms other than hydrogen

• Electrons do not move in circular orbits

7.4: EXAMPLE PROBLEM

Calculate the energy required to excite the hydrogen atom from level n=1 to level n=2. Also calculate the wavelength of the light that must be absorbed by a hydrogen atom in its ground state to reach this excited state.

• Answer: E = 1.633 E -18 J ; wavelength = 1.26 E -7 m

7.5: QUANTUM MECHANICAL MODEL

• Electron bound to nucleus similar to standing waves

• The exact path of the electron is not known

• Heisenberg Uncertainty Principle- a limitation to the position and momentum of a particle at a given time

7.5: QUANTUM MECHANICAL MODEL

Physical Meaning of ψ- Square of the function is the probability of finding an

electron near a particular point

- Represented as a probability distribution

- aka electron density map, electron density, electron probability

7.5: QUANTUM MECHANICAL MODEL

7.5: QUANTUM MECHANICAL MODEL

Radial Probability Distribution

Since the orbital size cannot be calculated, the size of the orbital is the radius of the sphere that an electron is in for 90% of the time

7.6: QUANTUM NUMBERS

Principal quantum number (n)• Main energy level• 1, 2, 3, …• Size and energy of orbital• When n increases: orbital becomes larger,

electron is further from the nucleus, higher energy b/c electron is less tightly bound to the nucleus so the energy is less negative

7.6: QUANTUM NUMBERS

Angular momentum quantum number/Azimuthal QN (l)• Sublevels, subshell• 0...n-1 for each value of n• Shape of atomic orbitals

7.6: QUANTUM NUMBERS

Magnetic quantum number ()• Integral values from l to –l • Orientation of the orbital in space

7.6: QUANTUM NUMBERS

7.7: ORBITAL SHAPES AND ENERGIES

• Size of orbital:

• defined as the surface that contains 9-% of the total electron probability.

• As n increases orbitals of the same shape grow larger .

7.7: ORBITAL SHAPES AND ENERGIES

• s Orbitals

• Spherical shape

• Nodes for s orbitals of n=2 or greater

7.7: ORBITAL SHAPES AND ENERGIES

• p Orbitals

• Two lobes each

• Occur in levels n=2 and greater

• Each orbital lies along an axis

7.7: ORBITAL SHAPES AND ENERGIES

• d orbitals

• Occur in levels n=3 or greater

• Four orbitals with four lobes each centered in the plane indicated in the orbital label

• Fifth orbital has two lobes along z axis and a belt centered in the xy plane

7.7: ORBITAL SHAPES AND ENERGIES

• f Orbitals

• Occur in levels n=4 and greater

• Complex shapes

• Usually not involved in bonding in compounds

7.7: ORBITAL SHAPES AND ENERGIES

Orbital Energies

• All orbitals with the same value of n have the same energy for hydrogen atoms (Degenerate)

• The lowest energy state = ground state

• When the atom absorbs energy the electrons can move to higher energy orbitals

• “excited state”

7.7 : QUESTION

Which Hydrogen atom shown has the highest energy?

7.8: ELECTRON SPIN AND THE PAULI PRINCIPLE

• Electron Spin Quantum Number

• An orbital can only hold two electrons, must have opposite spins.

• Spin can have +1/2 or -1/2

• Pauli Exclusion Principal

• In a given atom no two electrons can have the same set of four quantum numbers

7.9: POLYATOMIC ATOMS

• Polyatomic Atoms: Atoms with more than one electron

• Three energy contributions must be considered in description of the atom:

1) Kinetic energy of electrons as they move around the nucleus

2) Potential energy of attraction between nucleus and electrons

3) The potential energy of repulsion between the two electrons

7.9: POLYATOMIC ATOMS

• Electron correlation problem: Electron pathways are not known, so electron repulsive forces cannot be calculated exactly

• Average repulsions are approximated by...

• Treat each electron as it were moving in a field of charge that is the net result of the nuclear attraction and average repulsions of all other electrons

7.9: POLYATOMIC ATOMS

• Screening or Shielding

• Electrons are attracted to the nucleus

• Electrons are repulsed by other electrons

• Electrons would be bound more tightly if other electrons weren’t present

• Closer proximity to the nucleus = lower energy

7.9: EXAMPLE PROBLEM

What is the electron correlation problem?

Answer: Electron pathways are not known, so electron repulsive forces cannot be calculated exactly

7.10 HISTORY OF THE PERIODIC TABLE

• Originally constructed to represent patterns observed in chemical properties of elements

• Mendeleev and Meyer both independently conceived present periodic table

• Mendeleev also corrected several atomic masses

7:10: EXAMPLE PROBLEM

Which scientist is majorly credited with the creation of the modern periodic table?

• Answer: Dmitri Ivanovich Mendeleev

7.11: AUFBAU PRINCIPLE AND THE PERIODIC TABLE

• Aufbau Principle: “As protons are added one by one to the nucleus to build up elements, electrons are similarly added to these hydrogen like orbitals”

• Hunds Rule: “The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by Pauli principle in a particular set of degenerate orbitals

7.11: AUFBAU PRINCIPLE AND THE PERIODIC TABLE

• Periodic Table Vocab:

• Valence electrons: electrons in outermost principal quantum level of an atom

• Transition metals: “d” Block

• Lanthanide and Actinide Series : “f” block

• Representative Elements: Group 1A through 8A

• Metalloids: Border between metals and nonmetals, exhibit properties of both

7.11: EXAMPLE PROBLEM

• State the Aufbau principle :

• Answer: “As protons are added one by one to the nucleus to build up elements, electrons are similarly added to these hydrogen like orbitals”

7.12 PERIODIC TRENDS IN ATOMIC PROPERTIES

• See previous projects

• Ionization energy: energy required to remove an electron from an atomic (increase across period, decreases with increasing atomic number within a group)

• Electron affinity: energy change associated with the addition of an electron (decrease down period, increase across period)

• Atomic Radius: Determination of radius (increases down group, decreases across period)

7:12: EXAMPLE PROBLEM

• Order the atoms in each of the following sets from the least exothermic electron affinity to the most

• A) S, Se

• B) F, Cl Br, I

• Answers:

• A) Se, S ; B) I, Br, F, Cl

7.13: THE PROPERTIES OF A GROUP : THE ALKALI METALS

• Easily lose valence electrons

• Reducing agents

• React with water

• Large hydration energy

• Positive ionic charge