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Chapter 5: Electrons in Atoms 1 Section 5.1: Light and Quantized Energy Rutherford proposed that all of an atom’s positive charge and most of its mass are concentrated in the nucleus, surrounded by fast-moving electrons. major scientific development, but incomplete lacks detail about how electrons occupy space around the nucleus doesn’t explain why the negatively charged electrons are not pulled into the positivelycharged nucleus doesn’t account for differences in chemical behavior among elements Wave nature of light Electromagnetic radiation: form of energy that exhibits wavelike behavior as it travels through space. radio waves All EM waves travel at microwave 3.0 x 108 m/s in a infrared vacuum, represented by visible light “c” ultraviolet x-rays gamma Early 1900s, scientists observed certain elements emit visible light when heated in a flame. Chemical behavior is related to the arrangement of the electrons in the atoms Wavelength, represented by λ (lambda) Frequency, represented by ν (nu) = number of waves that pass a given point each second o measured in hertz (Hz) = 1 wave/s o Hz = 1/s (where wave is understood) or s-1 o Ex. 652 Hz = 652 waves/s = 652/s or 652 s-1 Amplitude: wave’s height from origin (or resting point) to crest or from origin to trough speed of light = wavelength x frequency c=λν Speed of all waves is the same, but may have different wavelengths and frequencies Wavelength and frequency are inversely related Sunlight is called white light – contains a continuous range of wavelengths and frequencies Passing through a prism separates the light into a spectrum of colors Short wavelengths bend more than long wavelengths ROY G BIV – colors of the spectrum Red – longer wavelength, less energy Violet – shorter wavelength, more energy Use c=λν to calculate wavelength or frequency of any wave. crest amplitude wavelength (λ) trough Visible light: red has longer wavelengths, lower frequency violet has shorter wavelengths, higher frequency Sample problem What is the wavelength (λ) of a microwave with a frequency of 3.44 x 109 Hz? c = λν c = λ v λ = 3.0 x 108 m/s 3.44 x 109 s-1 λ = 8.72 x 10-2m Practice problems: p. 121, #s 1-4 Chapter 5: Electrons in Atoms 2 Particle Nature of Light Aspects of light NOT explained by wave model: 1. Why heated objects emit only certain frequencies of light at a specific temperature. 2. Why some metals emit electrons when colored light of a specific frequency shines on them. a. Ex: iron at room temp is a dark gray iron when heated, glows red when heated further, glows blue Mathematically, energy of a quanta is related to the frequency (ν) of the emitted radiation. Energy = Planck’s constant x frequency E = hν h = Planck’s constant = 6.626 x 10-34 Js J = Joule (SI unit of energy) Energy increases as frequency increases. 1900, German physicist Max Planck studied light emitted from heated objects. Matter can gain or lose energy only in small, specific amounts called quanta. Quantum: minimum amount of energy that can be gained or lost by an atom Ex. Heating a cup of water in a microwave: temperature appears to rise in a continuous manner Actual temp increases in small, infinitesimal steps as its molecules absorb quanta of energy Because steps are small, it appears continuous rather than stepwise. Planck’s theory: for a given frequency (ν), matter can emit or absorb energy only in whole number multiples of hv (1 hv, 2 hv, 3 hv, etc.) Matter can only have certain amounts of energy Quantities of energy between these values don’t exist 1905 – Albert Einstein proposed the electromagnetic radiation has both wavelike and particle-like natures Sample problem: What is the energy of a photon from the violet portion of the rainbow if it has a frequency of 7.23 x 1014 s-1? Photon: particle of EM radiation with no mass that carries a quantum of energy A photon’s energy depends on its frequency Ephoton = hν Energy of a photon of light must have a certain minimum value (threshold) to cause the ejection of a photoelectron o For photoelectric effect to occur, the photon must have the minimum amount of energy required to free an electron from the atoms of the metal. Atomic Emission Spectra How neon lights work: pass electricity through a tube filled with neon gas Neon atoms absorb energy, become excited Pass the light emitted by neon atoms through a prism, and neon’s atomic emission spectrum is produced Atomic emission spectrum of an element: set of frequencies of EM waves emitted by atoms of an element Photoelectric effect: electrons (called photoelectrons) are emitted from a metal’s surface when light of a certain frequency shines on the surface. Ex. Solar calculator: photoelectric cells convert incident sunlight into electrical energy . Ephoton = hv Ephoton = (6.626 X 10-34 Js)(7.23 x 1014 s-1) Ephoton =4.79 x 10-19 J Practice problems: p. 124, #s 5-6 Neon has several individual lines of color – it’s not continuous. Each element’s atomic emission spectrum is unique. Can be used to identify that element Can determine the composition of an unknown compound. Behavior of light can only be explained by the dual wave-particle model! Chapter 5: Electrons in Atoms 3 Section 5.2: Quantum Theory and the Atom Niels Bohr worked in Rutherford’s lab DeBroglie’s Wave-Particle Duality 1913 – proposed the following while working with hydrogen (why hydrogen’s emission spectra was not continuous) 1924, Louis de Broglie proposed an idea that eventually accounted for the fixed energy levels of Bohr’s models Bohr’s quantized electron orbits had characteristics similar to waves o If waves can have particle-like behavior, can particles like electrons behave like waves? o If an electron has wavelike motion and is restricted to circular orbits of fixed radii (plural of radius), then the electron is allowed certain wavelengths, frequencies, and energies. DeBroglie developed an equation relating wavelength (λ) of a particle with mass (m) moving at a velocity (v) Atoms have only a finite number of energy states o Ground State – lowest possible energy state o Excited State – any other energy state o The more energy in an atom, the larger its orbits (the farther the electrons orbit away from the nucleus) o When an electron is in a higher energy orbit, it can move to a lower orbit by emitting a photon of equal energy to the difference between the energy levels ∆E = Ehigher-energy orbit ― Elower-energy orbit = Ephoton = hν o o Since electrons must move between well defined orbits, only certain frequencies of EM radiation can be emitted The emitted frequencies of light produce the emission spectrum of that element Bohr’s model works well for hydrogen, but not for the other elements. Bohr’s model is not widely accepted or currently used. Bohr’s model did provide the basis for quantum theory Errors in Bohr’s Models 1. Energy levels are similar to planetary orbits (circular) 2. Energy levels are equally spaced (like rungs on a ladder). Practical application of DeBroglie’s Wave-Particle Duality Wave – pencil in water appears bent or broken – automatic doors Particle – solar power Heisenberg’s Uncertainty Principle It is impossible to know both the exact position and velocity of a particle at the same time. λ=h or λ=h mv p DeBroglie’s equation predicts that all moving particles (like electrons) have wave characteristics. o proven by subsequent experiments o wave-like behavior and particlelike behavior of electrons cannot be observed at the same time DeBroglie’s Wave-Particle Duality explains radioactive decay: Alpha has both particle and wave properties o Particle properties do not provide enough energy to overcome nuclear attraction o Wave properties allow for existence outside the nucleus Schrodinger’s Wave Equation Furthered de Broglie’s wave-particle theory Equation treated hydrogen’s electron as a wave o Worked for other elements, also (Bohr’s model didn’t) Atomic model where electrons are treated as waves = wave mechanical model or the quantum mechanical model Chapter 5: Electrons in Atoms 4 Quantum mechanical model: Quantum Theory Key concept of Schrödinger's Equation is quantum numbers 1. Quantum numbers represent different energy states of electrons 2. Changes take place by absorbing/releasing photons 3. Electrons can occupy the same energy level without affecting each other Limits an electron’s energy to certain values Doesn’t describe the electron’s path around the nucleus The solution to Schrödinger’s wave equation is known as a wave function o wave function is related to the probability of finding the electrons in a particular volume of space around the nucleus o electrons are more likely in certain areas accounting for the shape of orbitals o atomic orbital: a 3-dimensional region around the nucleus that describes the electron’s probable location (fuzzy cloud) Energy Sublevels and Orbitals Sublevels – divisions within each of the principal energy levels Principal energy level 1 has 1 sublevel, level 2 has 2 sublevels, etc. o Number of sublevels is equal to the principal quantum number (n) of that level Sublevels are identified by the letters s, p, d, f o Beginning with level 4, sublevels will overlap o Letters are based on the original spectroscopy lines: s = sharp p = principal d = diffuse f = fundamental Each pair of electrons occupies an orbital: s=1 p=3 d=5 f=7 Maximum number of electrons in a sublevel: s = 2 p = 6 d = 10 f = 14 (each orbital can contain up to 2 electrons) Sublevels are preceded by the principal quantum number (for example: 1s, 3p, … Ex. Principal level 2 consists of 2s and 2p, level 3 consists of 3 sublevels: 3s, 3p, and 3d, level 4 consists of … Principal quantum numbers (n): Indicate the relative sizes and energies of atomic orbitals As n increases, the orbital becomes larger and the electron spends more time farther from the nucleus and the energy level increases Lowest principal energy level is assigned a principal quantum number of 1 (n = 1, electron is in its ground state) o n goes up to 7 Corresponds to the period number on the periodic table Greatest number of electrons that may occupy any level is 2n2. Hydrogen’s First Four Principal Energy Levels Principal quantum number (n) Sublevels (types of orbitals) present Number of orbitals related to sublevel 1 2 s s p s p d s p d f 1 1 3 1 3 5 1 3 5 7 3 4 Total number of orbitals related to principal energy level 2 (n ) 1 4 9 16 Chapter 5: Electrons in Atoms 5 Shape of the electron cloud Larger the principal quantum number (n), the larger the cloud Size is also determined by attraction of the nucleus and the repulsions of the other electrons All clouds in a level, when combined, will form a sphere Within the principal levels, orbitals can have different spatial orientations (m) (directions): p sublevel had 3 possible values (x, y, z oriented along the 3 coordinate axes) d sublevel has 5 possible values f sublevel has 7 possible values At any given time, an electron can occupy just one orbital. Hydrogen’s 1 electron in the ground state occupies the 1s orbital. If it gains a quantum of energy, it can move to the 2s orbital, to one of the 3p orbitals, or to another vacant orbital. Degenerate orbitals – orbitals of the same size and shape but different spatial orientation Section 5.3: Electron Configurations The arrangement of electrons follows a few very specific rules (with the occasional exception!) Electron configuration: the arrangement of electrons in an atom low-energy systems are more stable than highenergy systems electrons tend to arrange themselves in the lowest possible energy system ground-state electron configuration 3 rules (principles) define how electrons can be arranged in an atom’s orbitals. The aufbau principle: each electron occupies the lowest energy orbital available learn the sequence of atomic orbitals from lowest energy to highest energy In the diagram at left (textbook page 135), each box represents an atomic orbital. All orbitals related to an energy sublevel have equal energy (ex. all three 2p orbitals have equal energy) Energy sublevels within a principal energy level have different energies (ex. three 2 p orbitals have higher energy than the 2s orbital) o energy increases as the level changes In order of increasing energy: s, p, d, f Orbitals can overlap (ex. 4s has lower energy than 3d and will fill in first) Chapter 5: Electrons in Atoms 6 Each electron in an atom has a spin (like a top on its axis) The electron can only spin in 2 possible directions (↑↓) The Pauli exclusion principle: Only 2 electrons can occupy a single atomic orbital o electrons must have opposite spins Hund’s rule: single electrons with the same spin must occupy each equal-energy orbit before other electrons with opposite spins can occupy the same orbital Ex. One electron enters each of the three 2p orbitals before a second electron can enter any of the orbitals. Orbital diagrams and electron configuration notations: 2 methods for representing an atom’s electron configuration Method 1 Orbital diagram: includes a box for each of the atom’s orbitals. An empty box box containing a single up arrow down arrows ↑↓ ↑ is an unoccupied orbital. A represents an orbital with 1 electron. A box containing both up and represents a filled orbital. Each box is labeled with the principal quantum number and sublevel associated with the orbital. The number of electrons equals the number of protons, which is represented by the atomic number. Example: Carbon Atoms are not actually built electron by electron. Method 2: Electron configuration notation Designates the principal energy level and energy sublevel associated with each orbital Includes a superscript representing the number of electrons in the orbital Carbon looks like this: 1s22s22p2. See textbook, pg. 137, table 5-3 See page 138 for order of filling sublevels (next page of notes) What is the electron configuration notation for oxygen? Method 2b: Noble-gas configuration Helium: 1s2. *He+ also represents helium’s electron configuration Neon: 1s22s22p6. [Ne] Sodium is the first element in the 3rd principal level. Its configuration can be written as 1s22s22p63s1. Or, since sodium has the same electron configuration for its innermost electrons as neon, sodium can be written as [Ne]3s1. What is the electron configuration for magnesium? Chapter 5: Electrons in Atoms 7 Valence electrons: electrons in the atom’s outermost orbitals, generally those in the highest principal energy level electrons that are involved in the formation of chemical bonds Electron-dot structures: consists of the element’s symbol, representing both the element’s nucleus and its inner-level electrons surrounded by dots representing the atom’s valence electrons o dots are placed one at a time pair the s-level electrons first fill all remaining p-orbitals (one dot on each of the other 3 sides) before pairing up remaining electrons (see below)