Atomic Theory & Periodicity Chapters 6 & 7

Light How does an incandescent light bulb work?

Light Electricity is turned on Metal filament heats up Hot metal gives off light Blackbody Radiation

Blackbody radiation

Blackbody Radiation Max Planck proposed that the energy of light given off could only be emitted in little bundles, called quanta Bundles of light were multiples of a smaller unit E=h𝜈 h = 6.626 x 10-34Js Planck’s Constant

Photoelectric Effect Light shining on a photo-sensitive metal plate will emit electrons.

Photoelectric Effect Frequency must be above a minimum (threshold) frequency Brighter light (higher intensity) produces more electrons, but with the same energy Light with higher frequency will emit electrons with higher energy

Photoelectric Effect

Photoelectric Effect ℎ𝜈= 𝐾𝐸 𝑚𝑎𝑥 + 𝜙 Einstein expanded on Planck’s work to explain photoelectric effect Nobel Prize in 1921 Energy of Photon = Energy of ejected electron + work needed to eject electron (work function, Φ) ℎ𝜈= 𝐾𝐸 𝑚𝑎𝑥 + 𝜙

Atomic Model Review Dalton’s Hard Sphere Model Plum Pudding Model Atom is indivisible, indestructible sphere Plum Pudding Model Uniform positive sphere with negative electrons embedded within Rutherford Model Atom is mostly empty space, dense positive nucleus, electrons randomly outside nucleus

Bohr Model Rutherford Model could not explain chemical properties Niels Bohr proposed electrons in energy levels Valence electrons Electrons can move between energy levels by gaining or losing energy

Electron Transitions When electrons gain energy they move to higher energy levels When electrons drop to lower energy levels they release energy as light Energy is related to the distance between energy levels

𝑐=𝜆𝜈 𝐸=ℎ𝜈= ℎ𝑐 𝜆 Light Waves review Wave Equation Energy Equation Color is based on frequency, 𝜈 𝑐=𝜆𝜈 𝐸=ℎ𝜈= ℎ𝑐 𝜆

Electromagnetic Spectrum

Energy Practice Calculate the energy of a photon of yellow light that has a wavelength of 589 nm. Calculate the energy of a mole of photons of yellow light with a wavelength of 589 nm. 𝐸=ℎ𝜈= ℎ𝑐 𝜆 = (6.626 𝑥 10 −34 )(2.998 𝑥 10 8 ) 589 𝑥 10 −9 𝐸=3.37 𝑥 10 −19 𝐽 𝐸=(3.37 𝑥 10 −19 )(6.022 𝑥 10 23 ) 𝐸=2.03 𝑥 10 5 𝐽/𝑚𝑜𝑙

Quantum Mechanics Physics of the small New in the early 20th century High level math Thought experiments Led to many advances in technology

Schrödinger’s Cat Thought Experiment Cat, vial of poison, Geiger counter with radioactive sample in a sealed box. Can’t know if cat is alive or dead without interrupting the experiment (opening the box) The cat is considered BOTH alive and dead

Heisenberg Uncertainty Limit to what we can know The more precisely the momentum of a particle is known the less precisely the position can be known ∆𝑥∆𝑝≥ ℏ 2

Schrödinger Wave Equation Differential equation for wave functions of particles 𝑖ℏ 𝛿 𝛿𝑡 Ψ 𝑟,𝑡 =[ − ℏ 2 2𝑚 𝛻 2 +𝑉(𝑟,𝑡)]Ψ(𝑟,𝑡)

Wave Equation Solutions Solving the wave equation for an electron provides wave functions that include quantum numbers that describes where there is a high probability of finding an electron

Principle Quantum Number Denotes the principle energy level n Integers equal to or larger than 1 n = 1, 2, 3, …

Angular Quantum Number Denotes the sublevel within an energy level ℓ (lower case cursive L) Integers ranging from 0 to n–1 0 = s, 1 = p, 2 = d, 3 = f, 4 = g,….

Magnetic Quantum Number Denotes the orbitals in each sublevel mℓ Integers ranging from –ℓ to +ℓ ℓ = 0, mℓ = 0 (1 s orbital) ℓ = 1, mℓ = –1, 0, +1 (3 p orbitals) ℓ = 2, mℓ = –2, –1, 0, +1, +2 (5 d orbitals)

Spin Quantum Number Describes the magnetic property of the electron, “spin” ms ½ or –½

Pauli Exclusion Principle 2 electrons in an atom can’t have the same set of quantum numbers Each orbital can hold up to 2 electrons Must be different “spin”

Ψ2 Probability density and radial distribution function Describes the shape of an orbital

Orbitals

Orbitals

Orbitals

Electron Configurations Describes the number of electrons in an atom and their location 1s2 Number of electrons in sublevel Energy level Sublevel

Aufbau Principle Electrons will fill the lowest available orbitals Na 2-8-1 (Regents) 1s22s22p63s1 (AP)

Electron Config Examples Be 1s22s2 C 1s22s22p2 F 1s22s22p5 S 1s22s22p63s23p4

Electron Configurations Sublevels overlap each other More overlap the farther away from the nucleus K 1s22s22p63s23p64s1 4s sublevel is lower in energy than the 3d sublevel

Electron Orbital Configuration Sublevel order 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 5g 6s 6p 6d 6f 6g 6h 7s 7p 7d 7f 7g 7h 7i

Condensed Electron Config’s Sr 1s22s22p63s23p63d104s24p65s2 Use noble gas for inner electrons Sr [Kr]5s2

Orbital Diagram Visual representation Electrons as arrows H He Lines or boxes Electrons as arrows Different “spin”, different arrow direction H He 1s 1s

Orbital Diagram 1s 2s Li Be B 1s 2s 1s 2s 2p

Hund’s Rule Lowest energy is achieved when the number of electrons with the same spin is maximized C N 1s 2s 2p 1s 2s 2p

Electron Config Anomalies Because of how close in energy some sublevels are, some transition metals have partially filled ns sublevels with partially filled (n-1)d sublevels Sometimes ns = 0 Have to be determined experimentally

Electron Config Anomalies Cr [Ar]4s23d4 [Ar]4s13d5 Cu [Ar]4s23d9 [Ar]4s13d10

Magnetism Paramagnetism Diamagnetism Weak attraction to magnetic field due to unpaired electrons Diamagnetism Weak repulsion to magnetic field due to paired electrons

Photoelectron Spectroscopy Experimental method used to determine the electronic structure of an atom Photoemission Spectroscopy PES Based on the Photoelectric Effect specifically the Work Function

Photoelectric Effect (Review) Light shining on a photo-sensitive metal plate will emit electrons. Energy of Photon = Energy of ejected electron + work needed to eject electron (work function, Φ) ℎ𝜈= 𝐾𝐸 𝑚𝑎𝑥 + 𝜙

Photoelectron Spectroscopy Graph shows relative number of electrons and amount of energy required to remove them. Binding energy Often energy scale on x axis is reversed Zero to the right end Not always, have to pay attention!

Photoelectron Spectroscopy Inner most electrons Outer most electrons

Periodic Table Developed by Mendeleev in 1869 Initially arranged by atomic mass Certain elements rearranged by chemical properties Predicted missing elements with very accurate prediction of missing element’s properties

Periodic Table Henry Moseley determined atomic numbers using X-ray Spectroscopy Proved Mendeleev’s Periodic Table correct Died in WWI at age of 27 Most likely would have won 1916 Nobel Prize Not awarded to anyone in 1916

Periodic Table

Periodicity (Regents Review) Atomic Radius – Size of an atom Ionic Radius – Size of an ion Ionization Energy – energy required to remove outermost electron Electronegativity – ability to attract electrons while in a compound

Periodicity (Regents Review) Atomic Radius Decreases left to right Increases top to bottom Ionic Radius

Periodicity (Regents Review) Ionization Energy Increases left to right Decreases top to bottom Electronegativity

Periodicity (Regents Review) Metallic Character Decreases left to right Increases top to bottom

Periodicity (Regents Review) Valence Electrons Electrons in outermost occupied energy level Elements in same group have similar physical and chemical properties because they have the same number of valence electrons

Coulomb’s Law Electrons in an atom are attracted to the protons in the nucleus Electrons are also repelled by other electrons in the atom Attraction of outer electrons to nuclear protons is diminished by inner electrons “Shielding”

Effective Nuclear Charge, Zeff Actual attractive force felt by electrons Zeff = Z – S Z = nuclear charge S = shielding constant Approx = # of core electrons

Atomic Radius 2 types of measurements van der Waals radius = non-bonding Covalent radius = bonding radius

Atomic Radius Atomic Radius decreases across a period Additional electrons are in the same energy level Effective nuclear charge is increasing

Atomic Radius Atomic Radius increases down a group Additional electrons are in next higher energy level Effective nuclear charge doesn’t change (much)

Atomic Radius

Ionic Radius Metals tend to lose electrons when they form ions Valence electrons are lost The “new” valence electrons experience a larger effective nuclear charge, making them even smaller Less repulsion between electrons Na 1s22s22p63s1 Na+ 1s22s22p6

Ionic Radius Nonmetals tend to gain electrons when they form ions More valence electrons are added The “new” valence electrons experience a smaller effective nuclear charge, making them larger More repulsion between electrons F 1s22s22p5 F- 1s22s22p6

Ionic Radius For cations, ionic radius decreases across a period For anions, ionic radius decreases across a period Additional electrons are in the same energy level Effective nuclear charge is increasing

Ionic Radius Ionic radius increases down a group Additional electrons are in next higher energy level Effective nuclear charge doesn’t change (much)

Ionic Radius

Isoelectronic Series Ions have the same number of electrons Ionic radius decreases with an increasing nuclear charge

Ionization Energy Energy required to remove electron Each successive electron requires more energy to remove 1st < 2nd < 3rd < 4th….. After valence electrons, there is a large increase in energy to remove

Ionization Energy

Ionization Energy Ionization energy increases across a period Effective nuclear charge is increasing Atomic radius is decreasing Ionization energy decreases down group Valence electron is farther from nucleus Atomic radius increases

Ionization Energy

Ionization Energy Anomalies Transition from group 2 to group 13 Electron is removed from a farther out sublevel, p-sublevel instead of s-sublevel Transition from group 15 to group 16 Electron being removed from group 16 is from a paired orbital, resulting in a half-filled sublevel Repulsion due to pairing helps too

Electronegativity Electronegativity increases across a period Effective nuclear charge is increasing Atomic radius is decreasing Electronegativity decreases down group Atomic radius is increasing