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Chapter 1

Chapter 1.docx

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Department
Chemistry
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Chemistry 1027A/B
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Felix Lee

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Chapter 1: Atomic Theory Topic 1.1 Atomic Structure 1.1.2 A thief History -mid 19 century, scientists discovered that when hydrogen gas was placed in a tube and excited with a high-voltage electrical discharge, several colours of visible light were emitted. The Electromagnetic Spectrum -electromagnetic spectrum: the complete range of electromagnetic radiation that travels through space as energy in the form of oscillating waves -waves travel at the speed of light and are characterized by their wavelength (λ) or frequency (v) -frequency refers to the number of times a wave repeats itself in given amount of time -human eyes are only able to detect electromagnetic radiation between approximately 400-700nm (visible region) ( ) ( ) ( ) -the longer the wavelength, the lower the frequency -the shorter the wavelength, the higher the frequency Energy of Electromagnetic Radiation -energy of electromagnetic radiation is equal to frequency multiplied by plank’s constant where h is plank’s constant -there is in inverse relationship between wavelength and energy (longer wavelength=lower energy) -energy increases with increasing frequency Hydrogen Emission -Balmer equation predicts different visible emission wavelengths of hydrogen -Lyman equation predicts different UV emission wavelengths of hydrogen -Paschen equation predicts different infrared emission wavelengths of hydrogen 1.1.3 What is the Bohr Model? -based on data from the emission spectrum, Bohr proposed electrons in the H atom moved about the nucleus in a circular orbit -suggested multiple orbits exist and that the energy of each orbit was quantized (energy levels of the electron orbits have a discrete set of values) -Bohr assigned each orbit an integer n which is a fixed distance from the nucleus -as n increases, the energy difference between it and the next n level is less than between it and the previous level -Bohr’s explanation of hydrogen’s emission spectrum: -normally H’s electron occupies lowest energy level (ground state) -it is possible for the electron to absorb energy and be promoted to one of the higher levels (excited state) -this state is unstable -when electron returns to a lower energy level, the difference in energy is emitted as light of a wavelength corresponding exactly to the energy difference between the higher and lower levels -because there are many H atoms in a sample, different wavelengths are emitted, creating an emission spectrum -Deficiencies of the Bohr Model: Chapter 1: Atomic Theory -the Bohr model strictly treated electrons as particles, which is not entirely correct b/c electrons also behave as waves -when the spectrum was enlarged and carefully scrutinized, it was discovered that each line was actually split into two closely spaced lines, this type of splitting (fine structure) provided evidence for the magnetic and wave-like properties of electrons -it did not explain the relative intensities of the emission lines (eg. Why transitions from one specific higher level to a specific lower level were more probable than others) -failed miserably when applied to atoms with more than one electron around the nucleus 1.1.4 What is the Quantum Model? -particle-wave duality: according to quantum theory, light behaves as both a wave and a particle (photon) -electrons can also behave as both a particle and a wave—the quantum model looks at electrons as waves that are bound by the positively charged nucleus at the center of the atom -wave: a disturbance that travels through space and time, usually accompanied by a transfer of energy -two types of waves: -travelling: a disturbance that propagates in some direction -standing: a disturbance that repeats itself in time with no net translational motion -standing waves are fixed at both ends and can only oscillate at certain discrete frequencies -contain points, called nodes that remain fixed in space -different standing waves are mathematically described by wave functions, ψ (x) n st -first wave pattern ψ (1) corresponds to the fundamental frequency (1 harmondc) -second wave pattern ψ (x)2is 2 times the fundamental frequency (2 harmonic) -each harmonic corresponds to a discrete energy level (energies are quantized) nd -in the 2 harmonic and higher, nodes are present4 -nodes are points where the value of ψ(x) is zero , occurs when the wave switches from one phase to another at points other than the 2 fixed ends -Schrödinger developed an equation that allows one to predict the probability of finding an electron at a certain position in 3D space -this probability space around the nucleus is known as an orbital -orbital: specifies an area of space where the electron is most likely to be found -4 quantum numbers are used to describe the orbital of an electron in 3D space n, l, l, ms - n, l, and m refer to orbital, m refers to electron l s -obtained by solving the Schrödinger equation for the different wave functions -Pauli exclusion principle: no two electrons in an atom can have the same four quantum numbers Principal Quantum Number, n (wave function type [number of nodes]) -describes the type of wave function-> thus the number of nodes present in the wave -n= number of nodes in the wave +1 -as the value of n increases, the electron is higher in energy due to increasing frequency of the wave -electrons at higher n values have a greater probability of being found farther away from the nucleus -as n increases, so does energy and size of an orbital -historically n labels the electron shell Azimuthal Quantum Number, l (orbital number) -also known as the orbital angular momentum quantum number -describes the angular momentum of an electron in an orbital, the value of l defines the shape of the orbital -only specific values of l are permitted, from 0 to (n-1) Chapter 1: Atomic Theory -more shapes are possible at higher n levels because the orbital sizes increase with increasing n -l values are also refered to as sublevels -l values of 0,1,2,3 represent values respectively known as Sharp, Principle, Diffuse, and Fine Magnetic Quantum Number, m (orientalion on Cartesian plane) -magnetic quantum number refers to the orientation of an orbital on the xyz coordinate system -number of possible directions is dependent on the values of l -possible values of m range from –l to +l (including zero) l -each combination of n, l, and m relresent one orbital -each orbital can hold a maximum of 2 electron -all electrons with the same n and l numbers have the same energy -said to be degenerate Spin Quantum Number, m s -associated with spin and magnetism-> properties that all charged particles (ie electrons) posses -when one electron is spinning about an axis in a specific direction, a magnetic field in a specific direction perpendicular to the field is generated -reversing the spin also reverses magnetic field -there are 2 possible values for m ,s+1/2 and -1/2 -electrons in the same orbital must have opposite spins (to maintain Pauli Exclusion Principle) 1.1.5 What are the Shapes of the Orbitals? -in quantum mechanics, waves are used to describe the energy and/or locations of the electrons in an atom -mathematical wave functions are the simplest way to describe waves -wave functions are shown in 1D, it is actually 3D -orbital indicates the region of 3D space where the electrons are most likely to be found -with 1D wave functions, probability of finding an electron at a certain distance along the axis from the nucleus can be predicted by plotting electron density as a function of distance x away from the nucleus (can be derived from the square of the function), known as a probability plot See page 1-17 1.1.6 What are the Relative Energies of the Atomic Orbitals? -in quantum mechanics, energy levels are quantized and depend on the principal quantum number, n -all orbitals of the same n have wave functions of the same frequency or energy -only true for orbitals unoccupied by electrons -when an orbital closer to the nucleus is occupied by electrons, those electrons ‘shield’ positively charged nucleus from the electrons that are occupied in orbitals further away -further away electrons thus experience a weaker force -aufbau principle: electrons will occupy lower energy orbitals prior to filling orbitals of a higher energy -energy levels can overlap 1.1.7 What are Electron Configurations? -knowing relative energies of the orbitals, the ground state electronic arrangement of any atom can be written -in the ground state, the atom has an electron arrangement of the lowest possible energy -three methods are commonly used to convey information on electron arrangements -total number of electons represented must equal total number of electrons in the atom -electrons closest to the nucleus are written first Full Electron Configuration -electron configuration shows the number of electrons, as indicated by a superscript Abbreviated Electron Configuration -electron configurations are often abbreviated by using the noble gas electron configuration as “cores” Chapter 1: Atomic Theory
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