Atomic Orbitals and Quantum Numbers

• Chemistry is the study of matter's properties and behavior.
• Matter is anything that has mass and occupies space.

Elements and Atoms

• All materials are made from approximately 100 elements.
• Elements consist of chemically unique types of atoms.
• 118 elements are known, but heavier atoms are short-lived and not naturally found.

Atomic Theory Development

• Empedocles (c. 440 BC) proposed earth, fire, air and water as the fundamental components
• Democritus (460-370 BC) believed that the material world was made up of tiny, invisible, indivisible particles that they called ‘atomos', meaning “indivisible” or "uncuttable."
• Plato and Aristotle suggested the rejection of indivisible particles, influencing Western culture for centuries.

Dalton's Atomic Theory (1808)

• 1: Elements consist of indivisible particles called atoms.
• 2: Atoms of a given element are identical in mass and size, but differ from atoms of other elements.
• 3: Atoms cannot be transformed into different element atoms by chemical reactions; they are neither created nor destroyed.
• 4: Compounds are formed by combining two or more kinds of atoms in simple numerical ratios.
• Dalton's atomic model is known as the "Golf ball model".

Discovery of Electrons

• Johnstone G. Stoney named the fundamental unit of electricity "electrons" in 1891.
• William Crookes invented the Crookes tube, also known as a cathode ray tube, for studying electrical discharge in near vacuum.
• When two electrodes are connected to a high-voltage source, the cathode produces a stream of invisible radiation.
• Radiation emitted from the cathode is termed 'cathode rays'.
• Cathode rays can be deflected by a magnetic field and carry a negative electrical charge.

Properties of Cathode Rays

• Travel in straight lines and cast shadows.
• Consist of particles that possess mass and kinetic energy; they can rotate a paddle wheel.
• Are composed of negatively charged particles, deflected towards a positive electric field.
• Are affected by magnetic fields, with direction of deflection similar to other negatively charged particles.
• The nature of cathode rays does not depend on the gas or cathode material.
• The charge to mass ratio (e/m ratio) is constant for all gases.

Thomson's and Millikan's Contributions

• J. J. Thomson discovered that cathode rays are streams of negatively charged particles.
• Thomson calculated the charge-to-mass ratio of the electron: 1.76 x 10^8 coulombs per gram (C g^-1).
• Robert Millikan measured the charge of an electron as: 1.602 x 10^-19 C.
• Based on these values, the mass of the electron calculated as: 9.10 x 10^-28 g.
• The mass of the electron is about 1/1837 of a hydrogen atom.
• The relative charge of an electron is -1.

Discovery of the Nucleus

• Eugen Goldstein proved the existence of positive charges in matter.
• Using a perforated cathode in a discharge tube, a faint red glow was observed behind the cathode.
• The positive ions are attracted to the cathode, with some passing through the holes.

Properties of Positive Rays

• They travel in straight lines and cast shadows.
• Can move a paddle wheel.
• Are positively charged and are deflected by an electric field.
• Depend on the gas used in the discharge tube.
• Exhibit a variable e/m ratio depending on gas.

Key Discoveries About Atomic Particles

• Mass of a proton is 1.6 x 10^-24 g or 1.007276 u (atomic mass units).
• Relative charge of a proton is +1.
• Henri Becquerel discovered radioactivity in 1896.
• Lord Ernest Rutherford identified alpha (α), beta (β), and gamma (γ) emissions from radioactive materials indicating electric field bending.

Rutherford's Gold Foil Experiment and its Implications

• Conducted in 1908-09 by Rutherford, Geiger, and Marsden, using thin foils of gold and other metals as targets for α particles.
• Most α particles passed through undeflected.
• Some α particles were scattered at large angles.
• Few α particles bounced back.
• Atom is mostly empty space.
• Postive charge is concentrated in a dense central core, termed the nucleus.

Subsequent Atomic Structure Discoveries

• Masses of atoms were much greater than just protons and electrons using mass spectroscopy.
• Sir James Chadwick discovered the neutron in 1932.
• Neutrons have no charge, mass: 1.6749 x 10^-24 g or 1.008665 amu.
• Niels Henrik David Bohr combined existing ideas to suggest a nucleus surrounded by orbiting electrons.
• The electrostatic attraction equal to centrifugal force.
• This model was subsequently known as Rutherford-Bohr.
• Nucleons: particles found in the nucleus, including protons and neutrons.
• Nuclide: nucleus of an atom with specific numbers of protons and neutrons.
• Nuclides are composite particles of nucleons.

Atomic Number, Isotopes, and Mass Number

• Henry Gwynn Jeffrey Moseley found that the number of positive charges on the nucleus increases with atomic weight.
• Number of protons in an atom is an element's atomic number (Z).
• For a neutral atom, number of electrons equals number of protons.
• Atoms of an element with the same number of protons but differing numbers of neutrons are called isotopes
• Number of protons plus neutrons in an atom's nucleus is called the mass number.
• Mass number (A) is the sum of protons (Z) and neutrons.
• Atomic symbol designates mass number at top left, atomic number at bottom left.

Atomic Mass and Isotopes

• The atom of ^197Au has 79 protons, 79 electrons, and 118 neutrons.
• Atoms with identical atomic numbers but different mass numbers are isotopes.
• For example, carbon has isotopes ^12C, ^13C, ^14C.
• Stable isotopes are non-radioactive: unstable atoms will have radioactive isotopes
• mass unit (u) is convenient for extremely small masses of atoms
• 1 u is exactly 1/12 of a chemically unbound atom of carbon isotope ^12C.

Relative Atomic Mass

• Average atomic mass calculated from its isotopes: Σ [(isotope mass) x (fractional isotope abundance)].
• Example: Carbon's average atomic mass is 12.01 u based on abundances of ^12C and ^13C.
• When atomic mass is given as mass per mole of atoms in units of g mol-1 gives the molar mass
• Relative atomic mass (Ar) is the dimensionless ratio of average mass of an element's atoms to 1/12 the mass of carbon-12.

Ions

• Some atoms readily gain or lose electrons while the nucleus remains the same.
• Charged particle formed by electron removal or addition is called an ion.
• A positive charge means the atom has lost one or more elections
• A negative charge means the atom has gained one or more electrons
• A cation is positive; An anion is negatively charged.
• Atoms can gain or lose electrons to form monatomic ions.
• Charged molecules can form polyatomic ions.

Electromagnetic Radiation

• Much knowledge of electronic structure comes from analyzing emitted or absorbed light.
• Electromagnetic radiation (EMR) consists of synchronized oscillations of electric and magnetic fields, propagating at the speed of light through a vacuum.
• All types of electromagnetic radiation have wave-like characteristics.
• Light is one type of electromagnetic radiation.

Wavelength, Frequency and Energy

• Waves are periodic.
• Wavelength (λ): distance between two adjacent crests or troughs.
• Frequency (ν): cycles per second.
• Hertz (Hz) unit: cycles per second.
• Formula: c = λν.
• Speed of light (c): 2.998 x10^8 m s^-1.
• Quantization of energy: radiant energy either released or absorbed only in discrete quantities.
• Quanta: a minimum amount or quantity of energy.
• Electromagnetic spectrum: ordered display of electromagnetic radiation by wavelength.
• The energy E, of a single quantum, can be obtained by measuring how radiant energy is distributed.
• E=hv, where h is Planck's constant (Max Planck).
• Planck constant (h): 6.626 x 10^-34 J S.
• Radiant energy from a metal surface behaves like tiny energy packets called photons.
• Energy of a photon = E = hv.
• Louis de Broglie introduced the concept of matter exhibiting wave properties.
• Wavelength (λ) depends on mass (m) and velocity (v): λ = h / mv.

Ionization Energy

• Ionization energy of atom/ion is minimum energy to remove electron from isolated gaseous atom.
• Tells how much energy is needed to remove an electron.
• Ionization energies increase with successive electron removals.
• Sharp increase in ionization energy occurs with inner-shell electron removal showing energy levels are discreet.

The Hydrogen Spectrum

• Common radiation sources produce many wavelengths that make up a spectrum when separated.
• Continuous spectrum: range of colors by a source containing light of all wavelengths.
• Specific gases emit unique colors of light, which when passed through a prism, result in only a few wavelengths.

Line Spectrum

• Line spectrum: specific wavelengths from excited gases.
• Bohr combined existing ideas suggested that the atomic nucleus was surrounded by electrons moving in orbit.
• Rutherford-Bohr model or the Bohr model is used
• The electrons in order to remain in orbit, the electrostatic attraction between the nucleus and electron must be equal to the centrifugal force.
• Each orbit has a different value of n (n is a whole number).
• The smaller the n, the closer to the nucleus orbit is
• Line spectra result from emissions when electrons drop from initial to final energy levels.
• Formula: Ephoton = hv = hc/λ = -ΔE = (Ef - Ei)

Shapes of Atomic Orbitals

• Electrons probable location around atoms called orbitals, shows electron density distribution around the nucleus
• Electron density for s orbitals is spherically symmetrical and centered on the nucleus
• Each p subshell has three orbitals designated by their Cartesian axis direction

Quantum Numbers

• Three quantum numbers used to describe the orbital that electrons occupy in atoms and one that describes the spin of the electron: n, l, and ml and ms.
• The principal quantum number (n) defines the main energy level (shell); positive integer values.
• Angular momentum (l) has integral values from 0 to (n - 1), defining orbital shape (s, p, d, f)
• Magnetic quantum number (ml) has integer values between -l and l, describing orbital orientation.
• Spin quantum number (ms) has values of +½ or -½, indicating 2 charge directions which results in two opposite directions of electrical fields

Electron Configuration

• Shell consists of 1+ subshells each correlating to an allowed value of l
• Each s subshell consists of one orbital; each p subshell consists of three orbitals
• Each orbital corresponds to a different allowed value of ml.
• Total number of orbitals in a shell is n2

Aufbau Principle

• The filling begins with the subshell and continues upwards according to this principle.
• Fill electrons according to increasing energy levels.
• Orbitals with same energy are labelled degenerate

Pauli Exclusion Principle

• States no two electrons in an atom can have the same set of four quantum numbers.
• Each s subshell (one orbital) holds max two electrons. Each p subshell (three orbitals) holds max six electrons
• Electron configuration for lowest possible energy is known as the is in the ground state where the electrons are in the lowest possible energy state.

Hund's Rule

• For degenerate orbitals, lowest energy is when the number of electrons having same spin is maximized. That is electrons in one subshell all have same spin magnetic quantum number and these electrons arrangement results in parallel spins.
• Can be used to determine carbon

Condensed Configurations

• Writing just the noble gas up to core electrons. For example the [Ne]

Trends in the Periodic Table

• The periodic table shows the known elements.
• Each square gives the symbol, the atomic number and its mass

Organization of the Periodic Table

• Elements in are grouped in a series of ascending numbers
• Periods are the horizontal rows: Properties change
• The two left columns, the alkali alkaline earth, is where s orbitals are filled. These are also known as block
• Right hand columns, from group 3 to the group 8 make up what it is called the p-block.
• Elements in the d, block are called transation metals and
• The f, block are know as inner transation elements.

Periodic Properties

• Atomic properties depends are strongly dependent on the ability and strength of electrons
• The attractive force between an electron and the nucleus depends on the magnitude of charge of the nucleus
• Depends also on distance between the nucleus and the electron.

Screening Effect or Shielding Effect of Electrons

• Outer electrons of the atom are shielded from the nucleus by the inner electrons
• An electron experiences a net attraction that is less when electrons are present
• Results in an effective nuclear charge called Zeff

Sizes of Atoms and Ions

• Van der Waals Radius
  • One half the distance between two equivalent atoms with max attraction in a most stable arrangment
• Covalent radius
  • A chemical bond is the interaction between two atoms
  • Bonding atoms are closer than non bonding atoms
  • One of the bond is between these bonded is hald the bond distance
• Metallic radius
  • Between the nuclei of two adjacent metal atoms in metallic structure is metallic radius
  • Trend is atomic radii
    • Increase from top to bottom and decrease from left to right
    • This trend results from principal quantam numbers and increasing effective nulcear charge
    • Also note that there would be an opposite effect if these results do not exist

Ionization Energy

• Miniumum engery required to remove electron
  • Greater the ionization energy, greater the amount of energy
• Successive removes increase ionization
  • The nature depends on the atom

Election Gain Energy

• Energy change when electron is added
  • Most atoms release every when added
• Some atoms possess positive gain
  • Relatively stable configuration and addition is more difficult

Electronegativity

• Measure of atom ability to attract electric potential, greater means greater ability

Questions cover atomic orbitals and quantum numbers concepts. The description focuses on shapes of atomic orbitals and their quantum numbers. Also identifies the quantum number from Bohr model.