CHEM 131 textbook notes (Ch 1-3)
CHEM 131 textbook notes (Ch 1-3) CHEM 131 001
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Chemistry 131 Chapter 1 Atoms The properties of matter are determined by the structure of the atoms and molecules that compose them. 1.1 A Particulate View of the World: Structure Determines Properties - Two Main Points of chemistry • Matter is particulate—it is composed of particles • The structure of those particles determines properties of matter - Matter is anything that occupies space and has mass - Atoms are the basic particles that compose ordinary matter - When atoms bind together in specific geometrical arrangements, they form molecules - Chemistry is the science that seeks to understand the properties of matter by studying the structure of particles that compose it 1.2 Classifying Matter: A Particulate View - Substance is a specific instance of matter (air, water, sand) - The state of matter is the first classification • Depends on the relative position of particles and how strongly they interact with one another - The composition of matter is the second classification • Depends on the type of particles Fixed Volume States of Matter Fixed Shape Solid: particles are fixed in place and can only vibrate Liquid: particles are closely packed but can move past each other, allowing Fixed Volume liquid to flow and take shape of container No Fixed Shape Gas: particles are widely spaced, making gas compressible as well as fluid No Fixed Volume Compositions of Matter No Fixed Shape Pure Substance: - Made up of one type of particle (one component) - Composition is invariant (does not vary - Individual atoms or groups of atoms joined together Ex: helium (He), water (▯ ▯)! sodium chloride (NaCl) > Element a substance that cannot be chemically broken down into simpler substances (Helium, He) > Compound a substance composed of two or more elements in fixed, definite Most Common proportions (Water, ▯ ▯)! Mixture: - Made up of two or more particles - Composition can vary from one sample to another Ex: sweet tea can have a lot of sugar or a little > Heterogeneous the composition varies from one region of the mixture to another (water & sand, does not mix uniformly) > Homogeneous the composition is the same throughout the mixture (sweet tea, mixes uniformly) Matter Pure Substance Mixture Element Compound Heterogeneous Homogeneous Helium: Particles Water: Wet sand: two Tea w/sugar: two are atoms Particles are types of particles types of particles molecules that can be that mix distinctly thoroughly separated together 1.3 The Scientific Approach to Knowledge - Based on observation and experiment - Can be qualitative (noting/describing how a process happens) or quantitative (measuring or quantifying something about the process) Hypothesis à Experiments à Scientific Law - Scientific Laws describe how nature behaves—generalizations about what nature does - Scientific Theory a model for the way nature is and why - Most scientific observations are quantifiable and use units - A unit is a standard quantity by which to measure • Metric system • English system • International System of Units (SI) Table 1.1 SI Base Units Quantity Unit Symbol Length Meter M Mass Kilogram kg Time Second s Temperature Kelvin K Amount of Substance Mole mol Electric Current Ampere A Luminous Intensity Candela cd 1.4 Early Ideas about the Building Blocks of Matter > Leucippus & Democritus Many different kinds of atoms existed in different shapes and sizes > Plato & Aristotle Matter has no smallest part and different substances are composed of fire, air, earth, and water > Copernicus The sun is the center of the universe (scientific revolution) 1.5 Modern Atomic Theory and the Laws That Led to It Dalton’s theory, that all matter is composted of atoms, grew out of observations and laws - The most important laws led to the development/acceptance of atomic theory: 1) The Law of Conservation of Mass “In a chemical reaction, matter is neither created nor destroyed” Chemical reaction—process in which one or more substances are converted into one or more different substances S + Fe à FeS 32g 56g 88g Mass of reactants = Mass of products 2) The Law of Definite Proportions “A chemical compound always contains exactly the same proportion of elements by mass in any size” !"! !" ! Mass ratio = = 8.0 or 8:1 !! !" ! 3) The Law of Multiple Proportions “If two elements (A & B) form more than one compound, the mass of B combined with 1g of A will be a ratio of a whole number” Carbon Dioxide 1g carbon = 2.67g oxygen Carbon Monoxide 1g carbon = 1.33g oxygen !"#$%&:!"#$%& (!"#$%& !"#$"!%) !.!" !"#$%&:!"#$%& (!"#$%& !"#"$%&') = !.!! = 2 - John Daltons Atomic Theory 1. Each element is composed of tiny indestructible particles (atoms) 2. All atoms of a given element have the same mass & properties different to atoms of other elements 3. Atoms combine in simple, whole number ratios to form compounds 4. Atoms of one element cannot chance into atoms of another element. In chemical reaction, atoms only change the way they are bound together with other atoms Measurements of the relative weights of matter samples (1) before & after reaction, (2) different samples of the same compound, and (3) different compounds composed of same elements indicated that matter is particulate. 1.6 The Discovery of the Electron - All matter is composed of atoms but atoms are composed of even smaller particles Discovered > Cathode Rays (JJ Thompson) Electron - Particles that compose the Cathode Ray travel in straight lines - Independent of composition they originate from (Cathode) - Carry negative electric charge - Electron—a negatively charged, low-mass particle present within all atoms dDeduced charge > Oil Drop Experiment (Robert Millikan) of single electron -1.60 x 10 !!" C à charge of 1 single electron 9.10 x 10 !!" g à mass of 1 single electron 1.7 The Structure of the Atom Electron Plum-Pudding Model (Thompson) Sphere of Positive Charge - Radioactivity—emission of small energetic particles from the core of certain unstable atoms - Allowed researchers to experimentally probe the structure of the atom alpha (▯) particles ß positively charged, most massive beta (▯) particles gamma (▯) particles (+) Proton The Nuclear Atom (Rutherford) Neutron Nuclear Theory: 1. Most of the atoms mass & all of its (+) charge are in the nucleus [contains 99% of mass, but very little volume] 2. Most of the volume of the atom is empty space where (-) charge electrons are dispersed 3. There are as many (-) charged electrons outside the nucleus as there are (+) charged protons inside the nucleus - The atom also includes neutrons—neutral particles within the nucleus. Neutrons weigh the same as protons - Matter is mostly empty space but appears solid because the variation in its density is on a scale too small for our eyes to see 1.8 Subatomic Particles: Protons, Neutrons, and Electrons (+) Protons 1.67262 x 10 !!" kg see this) Neutrons 1.674393 x 10 !!"kg } Approx. 1 amu me !!" (-) Electrons 0.00091 x 10 kg } 0.00055 amu - The proton and electron both have the same charge (-1.60 x 10 !!" C) but opposite in sign (+/-) * All atoms are composed of the same subatomic particles but the number of protons defines the element - The number of protons in an atoms nucleus is its atomic mass (Z) - Each element, along with their atomic number, also has a chemical symbol—a 1 or 2 letter symbol (He, C) Isotopes . * All atoms of an element have the same protons but not always the same neutrons. These are called isotopes. - The relative amount of each different isotope in a naturally occurring sample of an element is its natural abundance - The number of neutrons and protons in an atom is its mass number (A) - Isotopes are symbolized as: Mass number à ! ß chemical symbol Ex: ▯▯ !"▯▯ !"▯▯ Atomic number à ! ▯ !" !" !" or: chemical symbol à X-A ß mass number Ex: Ne-20 Ne-21 Ne-22 Ions - The number of electrons in a neutral atom is equal to the charge of its nucleus - During chemical changes, atoms can gain or lose electrons and become charged particles called ions Cations—positively charged ions (metals) Anions—negatively charged ions (nonmetals) - Ions behave differently than the atoms from which they are formed because the structure of particles (and the charge) determines their properties. 1.9 Atomic Mass: The Average Mass of an Element’s Atoms - The average mass of an element is its atomic mass - This number comes from the average mass of all the isotopes in a given element weighted according to the natural abundance Atomic Mass = 0.7577(34.97amu) + 0.2423(36.97amu) = 35.45amu of Chlorine Cl-35 Cl-37 - The masses of atoms & percent abundance of isotopes of elements are measured using mass spectrometry—technique that separates particles according to mass - Mass spectrometry is graphed as the mass of the isotope that was ionized and the intensity indicating the relative abundance of the isotope )100 i 50 107 n Silver (Ag) n 109 I 0 } Mass (amu) - The percentage of each isotope is determined by the intensity of each line. But the total intensity must be normalized—made to equal 100% - To do this, divide intensity of each peak by total intensity: Abundance of 100% = x 100% = 51.84% Ag-107 100% + 92.90% Abundance of = 92.90% x 100% = 48.16% Ag-109 100% + 92.90% 1.10 The Origin of Atoms and Elements Big Bang Theory - Birth of the universe - Hot, dense collection of matter and energy that expanded rapidly and cooled to form hydrogen & helium (the most abundant elements in the universe Chemistry 131 Chapter 2 Measurement, Problem Solving, and the Mole Concept 2.1 The Metric Mix-Up: A $125 Million Unit Error - Quantification is the assignment of a number to some property of a substance or thing (ex: a 16cm pencil) - On Dec 11, 1998, NASA launched the Mars Climate Orbiter. A unit mix-up caused the Orbiter to enter Mars’ atmosphere at an altitude too low. Instead of orbiting, it disintegrated, costing $125mill. 2.2 The Reliability of a Measurement - The reliability of a measurement depends on the instrument used to make the measurement (a butcher scale is more precise than a bathroom scale) more digits = more certainty less digits = less certainty - Scientific measures are reported so that every digit is certain except for the last, which is estimated 5.213 certain^ ^estimated - The number of digits reported depends on the measuring device 10.5g on one scale is 10.4977 on another There are two kinds of certainty in science: 1. Accuracy how close the measurement is to the actual value 2. Precision how close a series of measurements are to one another 2.3 Density -The density of a substance is the ratio of its mass (m) to volume (v) Density = !"## o !"#$%& - Density is an intensive property of a substance—it is independent of the amount of the substance - Mass is an extensive property of a substance—it is dependent of the amount of the substance SI unit for density: kg/m ! Density is often displayed as: g/cm or gmL 2.4 Energy and Its Units - Two fundamental components of the universe are matter and energy - Energy is the capacity to work - Work is an action of force through a distance - The total energy of an object is the sum of its kinetic energy (energy associated with its motion) and its potential energy (energy associated with its position/composition) - Thermal energy is a type of kinetic associated with the temperature of an object Potential Energy à Kinetic Energy à Thermal Energy Principles of Energy: - Energy is neither created nor destroyed - The tendency of systems with high potential energy to change in a way that lowers their potential energy • Objects or systems with high potential energy tend to be unstable - Chemical potential energy arises primarily from electrostatic forces between the electrically charged particles (protons & electrons) that compose atoms and molecules - The structure of a molecule determines the potential energy Kg To Find Kinetic Energy: ! ems ! KE = ! mv - The SI unit of mass (m) is kg and velocity (v) is m/s à The SI unit of energy is kg ∙ m /s (joule, J) - One joule is very small so kJ is often used 1 kJ = 1000 J à Another unit of energy is the calorie 1 cal = 4.184 J - Not to be confused with the nutritional Calorie (uppercase C) 1 Cal = 1000 cal à The transfer of energy is always from the point of view of the system under observation ex: dropping a weight (system), weight falling loses energy to its surroundings (anything with which the system interacts) When the system loses energy: Exothermic (-) When the system gains energy: Endothermic (+) 2.5 Converting Between Units - Dimensional Analysis—using units as a guide to solve problems - Conversion Factor—fractional quantity with units you are converting from on the bottom and units you are converting to on the top given unit × !"#$%"! !"#$ = desired unit !"#$% !"#$ 2.6 Problem Solving Strategies To Solve Any Problem: • Identify the starting point (the given information) • Identify the end point (what must be found) • Devise a way to get from start to end (the conceptual plan) Units Raised to A Power: - Remember to raise both the number and unit to the power 2.54cm = 1in (2.54cm) = (1in) ! ! ! 6.45cm = 1in 2.7 Solving Problems Involving Equations - A conceptual plan is used to show how the equation takes us from the given (start) quantities to the find (end) quantities ! d = ! 2.8 Atoms and the Mole: How Many Particles The Mole: - a mole (mol) is the amount of material containing 6.02214 × 10 particles !" 1 mol = 6.02214 × 10 particles ^Avogadro’s Number à One mole of anything is 6.02214 × 10 units of that thing (usually rounded to 6.022 × 10 ) " The value of the mole is equa!"to the number of atoms in exactly 12g of pure carbon (12g C = 1 mol = 6.022 × 10 C atoms) Number of Moles and Number of Atoms Conversion: !" ! !"# !"#$% or .!"" × !" !"#$% !.!"" × !" !"!"#$% ! !"# !"#$% Mass and Amount (Number of Moles) Conversion: - To count atoms by weighing them, mass is needed - The mass of 1 mol of atoms is the molar mass An elements molar mass in grams per mole is numerically equal to the element’s atomic mass in atomic mass units (amu) Ex: mass of copper (63.55 amu) Molar mass of copper (63.55g/mol) 1 mol of copper (63.55g) Chemistry 131 Chapter 3 The Quantum-Mechanical Model of the Atom 3.1 Schrodinger’s Cat - Electrons are the smallest particles that make up matter - The absolutely small (quantum) world of the electron behaves differently than the large - When unobserved, quantum particles like electrons can be in two different states at the same time - Quantum-Mechanical model of the atom describes electrons as they exist within atoms 3.2 The Nature of Light - Light has many characteristics in common with electrons, such as wave-particle duality (certain properties of light as best described as a wave or particle) Wave Nature of Light - Light is electromagnetic radiation, energy embodied in oscillating electric and magnetic - Magnetic Field: a region of space where a magnetic particle experiences a force (space around magnet) - Electric Field: region of space where an electrically charged particle experiences a force (proton has electric field around it) ∎Speed of light (c): 3.00×10 m/s ∎Speed of sound: 340 m/s - A wave is characterized by its amplitude and wave.ength Amplitude vertical height of a crest, determines light’s intensity (brightness) Wavelength (▯) distance between crests, determines color - Light is also charac!!rized by its frequency (▯), the number of cycles (wave crests) in a - Frequency is inversely proportional to the wavelength (▯) Formula: of ▯ spelight frequency - ▯ = - The different colors in visible light—light seen by the human eye—corresponds to the different wavelengths (frequencies) The Electromagnetic Spectrum - Electromagnetic spectrum is a chart of all the wavelengths 'f electromagnetic radiation freq;fVcy 04 106 108 microwave012 1014 1016 1018 1020 102 1024 Radjd infrared 4¥41, x.ray gamma ray wavelength --nKȾ<=¥÷÷KȾ-><= XKA 105 103 10 10-1 103 10's 1 10 00 . 79 1 10'D lots > Gamma Rays (▯) - Shortest wavelength (m) - Produced by sun, stars, unstable atomic nuclei - Dangerous to humans (damage biological molecules) > X-rays - Wavelength (<10nm) - Used to image bones and internal organs - Can be dangerous in over exposure > Ultraviolet (UV) Radiation - Wavelength: 400nm – 10nm - Component of sunlight that produces sunburn/tan - Excessive exposure can cause skin cancer > Visible Light - Wavelength: 750-400nm - Involves all the colors we can see—the rainbow - Is not damaging to humans > Infrared (IR) Radiation - Wavelength: 1mm-750nm - Heat felt when near hot object - Can be detected in infrared sensors (night vision) > Microwaves - Wavelength: 187mm-1mm - Used for radar and microwaves - Absorbed by water and heats substances containing water > Radiowaves - Wavelength: 600m-187mm - Longest wavelength - Produce radio, all phones, tv Interference and Diffraction - Waves interact with each other through interference: cancelling each other out or building each other up, depending on alignment 1. Constructive interference - When two waves of equal amplitude are in phase when they interact - Align with overlapping crests (double amplitude) waves in ~ constructive ~ N interference p ase 2. Destructive interference - When two waves are out of phase when they interact - Align with crest from one overlaps trough of the other ~ - destructive wafts:L - interference - Waves also exhibit diffraction—when a wave encounters an obstacle or slit that is comparable in size to its wavelength, it bends (diffracts) around it - An interference pattern is the diffraction of light through two slits separated by a distance comparable to the wavelength of the light The Particle Nature of Light - The photoelectric effect is the observation that many metals emit electrons when light shines upon them. This can be measured as an electrical current - Binding energy is the energy with which the electron is bound to the metal - High frequency, low intensity light produces electrons without lag time - The amount of energy (E) depends on frequency (▯) E = h▯ !!" ∎ (h) is Planck’s constant: 6.626×10Js - A packet of light is called a photon or a quantum of light - Energy can also be expressed as Epvlsef =# of E = !" Ephoton ! - For an electron bound to the metal with binding energy ϕ, the threshold frequency is reached when energy of photon = ϕ Threshold Frequency Condition h▯ = ϕ - As the frequency of the light increases over the threshold frequency, the excess energy of the photon transfers to electron as kinetic energy KE = h▯ − ϕ 3.3 Atomic Spectroscopy and the Bohr Model - Atomic spectroscopy is the study of the electromagnetic radiation absorbed and emitted by atoms Atomic Spectra photo - When an atom absorbs energy (heat, light, electricity) it often re-emits that energy as light - Light emitted by various atoms contain distinct wavelengths - Passing light emitted by a single element through a prism results in a series of bright lines called emission spectrum - The emission spectrum is specific to each element and can be used to identify them - The Rydberg equation predicts the wavelength of emission spectrum 1 = (1.097×10 ▯ )( 1 .− 1 ) m & n can also be writ▯! (final) ▯ ▯ ! ▯! and▯! (initial) for stages of electron Rydberg Constant Integers The Bohr Model Stationary States - Electrons travel around nucleus in specific, fixed, circular distances from nucleus - Energy of each orbit is also fixed (quantized) - No radiation is emitted by electron in “stationary state” - When electron jumps (transitions) from one state to another, radiation is emitted or absorbed - Electron is never absorbed between states, only in one or another - The Bohr Model was not fully accepted & eventually replaced Atomic Spectroscopy and the Identifications of Elements - The presence of intense lines in the spectra of a number of metals is the basis for flame tests, simple tests used to identify elements in ionic compounds - The emission of light from elements is easier to detect, the absorption of light by elements is more commonly used - Absorption spectrum is dark lines on a bright background - Measured by passing white light through a sample and observing what wavelengths are missing due to absorption - Plots the intensity of absorption as a function of wavelength 3.4 The Wave Nature of Matter - The wave nature of electrons replaced Bohr’s Model - The wave nature of the electron is seen most clearly in diffraction - The interface patter is not caused by pairs of electrons interfering with each other, but by single electrons interfering with themselves - The wave nature of electrons is an inherent property of individual electrons Three Important Manifestations of Electron Wave Nature (1) The de Broglie Wavelength - A single electron has wave nature; its wavelength is related to its kinetic energy fast electron = high kinetic energy = short wavelength - The wavelength (▯) of an electron of mass “m” moving at velocity is “v” the de Broglie relation: (9.11×0354) ℎ messofelectnfw ▯ = ▯▯ , (2) The Uncertainty Principle - We can never both see the interference pattern and simultaneously determine which hole the electron goes through (cannot see wave nature & particle nature simultaneously) - Wave nature & particle nature of electrons are complimentary properties—they exclude each other - The velocity of an electron is related to its wave nature - The position of an electron is related to its particle nature - We cannot simultaneously measure an electrons position and its velocity with infinite precision Heisenberg’s Uncertainty Principle ℎ ∆▯ × ▯∆▯ ≥ momentum 4▯ ∆▯ = uncertainty position ∆▯ = uncertainty velocity m = mass of particle h = Planck’s constant (3) Indeterminacy and Probability Distribution Maps - Newton’s law of motion is deterministic—the present determines the future - Position & velocity required to predict trajectory ∎ This does not work for electrons! - In quantum mechanics, trajectories are replaced with probability distribution maps— statistical map showing where an electron is likely to be formed under certain conditions Quantum mechanical Classical trajectory :÷÷ ÷:÷:÷ probability distribution map - The characteristic of electrons landing in random/unpredictable places is interdeterminacy—path only described statistically 3.5 Quantum Mechanics and the Atom - Position-and energy are also complimentary properties - When given energy, we cannot know position of electron precisely. A guess of the electrons position is its orbital—probability distribution map showing where electron is likely to be found - The equation of energies and orbitals: ▯▯ = ▯▯ H = Hamiltonian operator (total energy KE and potential in electron) E = Actual energy of electron ψ = Wave function—mathematical function that describes the wave-like nature of electron - A plot of the wave function (ψ ) represents an orbital Solutions to the Schr▯dinger Equation for the Hydrogen Atom - Each orbital is specified by three interrelated quantum numbers ▯ ▯ ▯ ! intent principal angular momentum magnetic : - A fourth quantum number, ▯▯ the spin quantum number specifies orientation of the spin of the electrons à The Principal Quantum Number (▯) - Integer that determines the overall size and energy of an orbital ∎ Possible Values: ▯ = 1, 2, 3… ex: Hydrogen atom ! ▯!= −2.18×10 !!"▯ ( ! (▯ = 1, 2, 3…) - Energy is negative because the electron’s energy is lowered (−) by its interaction with the nucleus !!" - (-2.18×10 J) is Rydberg’s constant for Hydroge! (▯ ) - Orbitals with higher values of ▯ have greater (less negative) energies à The Angular Momentum Quantum Number (▯) - Integer that determines the shape of the orbitals ∎ Possible Values: ▯ = 0, 1, 2, …, (▯ −1) Value of ▯ Letter Designation ▯ = 0 s ▯ = 1 p ▯ = 2 d ▯ = 3 f - Values of ▯ beyond 3 are in alphabetical order ex: ▯ = 4 à g, ▯ = 5 à h à The Magnetic Quantum Number (▯ ) ▯ - Integer that specifies the orientation of the orbital ∎ Possible Values: ! = −▯ – 0 – +▯ ex: ▯ = 1 à ▯!= -1, 0, +1 ▯ = 3 ! ▯ = -3, -2, -1, 0, +1, +2, +3 à The Spin Quantum Number (▯ ) ▯ - Specifies orientation of the spin of the electron - Electron spin—fundamental property of an electron (all electrons have the same spin) ! ∎ Spin up: (▯ =!+ ) ! ∎ Spin down: (▯ = ! ) ! ! - Each specific combination of the quantum numbers ▯, ▯, and ▯ spe!ifies one atomic orbital ex: ▯ = 1, ▯ = 0, ▯ = 0 à 1s orbital ! 1: value of ▯ s: ▯ = 0 !▯ = 0 - Orbitals with the same value of ▯ are in the same principal level or principal shell - Orbitals with the same value of ▯ and ▯ are in the same sublevel or subshell Ø The number of sublevels is equal to ▯ ▯ = 1 à one sublevel (▯ = 0) ▯ = 2 à two sublevels (▯ = 0,▯ = 1) Ø The number of orbitals in a sublevel is equal to ▯▯ + ▯ S sublevel (▯ = 0) à [2(0)+1] à one orbital P sublevel (▯ = 1) à [2(1)+1] à three orbitals Ø The number of orbitals in a level is equal to ▯ ▯ ▯ = 1 à one orbital ▯ = 2 à four orbitals Principal Level (▯) Sublevel (▯) ▯ = 1 ▯ = 0 1s = ◻ ▯ != 0 2s = ◻ ▯ = 2 ▯ = 0 ▯ != 0 ▯ = 1 2p = ◻ ◻ ◻ ▯ != -1, 0, +1 ▯ = 3 ▯ = 0 3s = ◻ ▯ != 0 ▯ = 1 3p = ◻ ◻ ◻ ▯ = -1, 0, +1 ! ▯ = 3 3d = ◻ ◻ ◻ ◻ ◻ ▯ != -2, -1, 0, +1, +2 Atomic Spectroscopy Explained - Each wavelength in the emission spectrum of an atom corresponds to an electron transition between quantum-mechanical orbitals - When an atom absorbs energy, an electron in lower energy orbital is excited— it moves to a higher level - When an atom releases energy, an electron in higher energy orbital relaxes to a lower level (orbital) - This reaction releases a photon of light containing an amount of energy equal to the difference between two energy levels 1 1 ∆▯ = −2.18×10 !!" ▯ ( ! − !) ▯!nn ▯ ! orbitals far apart = higher energy = shorter wavelength 3.6 The Shapes of Atomic Orbitals - Chemical bonds depend on the sharing of electrons - The shape of an atomic orbital is determined by ▯ s Orbitals (▯ = ▯) - Lowest energy orbital - Wave function squared (Ψ ) is the probability density—the probability of finding an electron in a plot of space !"#$%$&'&() Ψ = probability density = ! !"#$ !"#$%& - The magnitude of Ψ is proportional to density of dots - To get a better idea of where the electron is most likely to be found, we use the radial distribution function (RDF), which represents the total probability of finding the electron within a thin spherical shell at a distance “r” from the nucleus !"#$%$&'&() total radial probability (at a given r) = × volume of shell at r !"#$ !"#$%& - The function represents the total probability at a radius r - The RDF has value of zero at nucleus • Increases to maximum 52.9pm them !!" • Decreases with increasing r (1pm = 10 m) - The shape of RDF is the result of multiplying two functions with opposite trends in r 1. PDF (Ψ ), probability per unit volume, has a maximum at nucleus and decreases with increasing r 2. Volume of thin shell, zero at nucleus and increases with increasing r - Orbitals greater than 1s contain at least one node—a point where the wave function (Ψ) and probability density (Ψ ) and RDF all go through zero p Orbitals (▯ = ▯) - Each principal level with ▯ = 2 or greater contains three p orbitals (▯ ! −1,0,+1) - Not spherically symmetric - Have two lobes of electron density on either side of the nucleus w/ a node at the nucleus d Orbitals (▯ = ▯) - Each principal level with ▯ = 3 or greater contains five d orbitals (▯ = −2,−1,0,+1, +2) ! - Cloverleaf shape with four lobes of electron density around nucleus and two perpendicular nodal planes f Orbitals (▯ = ▯) - Each principal level with ▯ = 4 or greater contains seven f orbitals (▯ ! -3, -2, -1, 0, +1, +2, +3) The Phase of Orbitals themfi# One dimensional - The sign of the amplitude of a wave its phase - Phase determines how it interferes with other waves . " ' 25 oh Three dimensional .tl#&j ' sorbitd Shape of Atoms - Atoms are drawn as spheres because most atoms contain many electrons occupying a number of different orbitals - Shape of atom is formed by superimposing all of its orbitals
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