Chemistry Chapter 2.1 PDF

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2.1 Atomic Structure

Electromagnetic Waves • Are oscillations of an electromagnetic field that propagate through space at the speed of light — C = 299 792 458 m s (in vacuum) • Simple periodic waves are characterized by wavelength (λ) or frequency (V) • Wavelength refers to the distance between two closest equivalent points of the wave o Usually expressed in units of length o Measured from peak to peak • Frequency refers to the number of oscillation cycles that occur at a fixed point in one second o Unit of frequency is s or Hertz (Hz) • Shorter wavelength = higher frequency, bc more waves are able to pass a fixed point in one second, therefore longer = lower • Freq. and WL of electromagnetic waves are related through: V = c/λ o Where c is the speed of light • Simple periodic waves propagating along an axis can be described by a sine function • Amplitude (Ψ) is the “height” of a wave, o Square of the amplitude = wave’s intensity o Higher amplitude = brighter, lower = dimmer -1

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Electromagnetic Spectrum • The complete range of wavelengths (frequencies) of electromagnetic radiation • Wavelength the only characteristic distinguishing different forms of electromagnetic radiation o Different wavelengths of light produce different colours • Most wavelengths in the spectrum are invisible to the human eye • Visible region/spectrum is between 400-750 nm o Wavelengths of light in this region range from violet-red, in rainbow order

Energy of Light • Light is a stream of energy that behaves like a wave or as particles • Photons are tiny packets of energy that carry fixed amount of energy related to it’s frequency (V) and wavelength (λ) o Relation represented by: E = hv = hc/λ o h = 6.6260696 x 10 J(s), h is known as the Planck constant  Shorter wavelength = greater energy possessed by photons, and vice versa • Atoms and molecules can only absorb/emit whole protons o When a photon is absorbed by a system it’s energy increases, and when it emits one the system energy decreases (equal to E = hv) -34

Take Away: a) light is a stream of photons that can behave as waves or as particles b) Energy of light can be absorbed or emitted only as small discrete portions c) Energy of each photon is determined by its frequency (or wavelength)

Emission Spectrum of Atomic Hydrogen • Balmer Series: the series of spectral lines emitted by hydrogen as visible light at wavelengths (nm) 410, 434, 486, 656 • Lyman Series: the discrete wavelengths emitted by hydrogen as ultraviolet light as 97, 102, 122,..nm • Paschen Series: the discrete wavelengths of infrared light emitted by hydrogen atoms • All wavelengths of light emitted by excited H atoms can be predicted exactly by: 1/λ = RH [(1/n2) - (1/m2)] o n and m are integers (n ≥ 1, m > n) and R = 10973731.6 m is a constant known as the Rydberg constant o n = 1 & m = 2,3,.. gives Lyman wavelengths, n = 2 & m = 3,4,.. give Balmer series, n = 3 & m = 4,5,.. gives Paschen series • On a spectrum, shorter wavelengths always go to the left, longer to the right -1

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The Bohr Model of the Hydrogen Atom • Proposed that the electron in the H atom moves about the nucleus in a circular orbit • Postulated only certain orbits are possible, so energy of e in each orbit is “quantized” • Each orbit/energy level assigned an integer index n = 1,2,3,…, with 1 being orbit closest to the nucleus o Energy of electron in n orbit: E = –(R /n )hc o As n increases, energy difference between consecutive levels decreases • Hydrogen’s electron usually occupies n=1 (ground state) o Excited state is when the electron absorbs energy of the electric discharge and goes to a higher level (m) o Excited state is unstable o When electron returns to lower level, energy difference is emitted as light with wavelength corresponding to energy difference between the levels involved  E – E = R [(1/n ) - (1/m )]hc = hc/λ  Results in Rydberg formula • Lyman, Balmer, and Paschen series are due to transitions from higher (m) to lower levels (n=1, n=2, n=3, respectively) 2

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Problems with the Bohr Model 1. Strictly treated electrons as particles, but electrons also behave as waves 2. Was demonstrated that the emission spectrum could be altered by placing the sample in a magnetic field - Bohr model didn’t explain this 3. Intensity of lines couldn’t be explained. This is directly related to why transitions from one specific (higher energy) level to a lower level were more probable 4. The model didn’t work when applied to atoms with more than one electron. Only for “hydrogenic atoms” 5. Doesn’t explain how electron stays in n=1 w/o falling to nucleus, or why only certain orbits are allowed

The Quantum-Mechanical Model • Must treat electrons as waves

Diffraction and Interference of Waves • Diffraction a phenomenon shown by a wave passing through a slit in a barrier (width comparable to the wavelength), and expanding to fill all space on other side of barrier • Constructive Interference occurs when two interacting waves are “in phase” (maxima and minima aligned). Results in wave w/ amplitude the sum of the amplitudes of the two waves • Destructive Interference occurs when two interacting waves are in opposite phases. Results in wave with zero amplitude…waves cancel each other out The Two-Slit Experiment • Helps to distinguish particles from waves • Light beam approaches two closely spaced slits, passes through, secondary light waves propagate in all directions (diffraction) and produces interference pattern o An alternation of bright/dark bands, results of constructive/destructive interference • If done with particle stream instead of light beam, two bright bands but no interference pattern appears De Broglie Waves and Particle-Wave Duality • Suggested electrons may exhibit wave-like behaviour in addition to their particle-like properties • Related mass (m) and velocity (v) of a particle to it’s wavelength: λ = h/mv o To be measurable, m/v must be very small, only microscopic particles like electrons Electrons as Standing Waves • Quantum Mechanics, aka wave mechanics, treats electrons in an atom as waves • Waves are disturbances that travel through space and time, usually accompanied by an energy transfer • Travelling Waves is a disturbance in which every point undergoes oscillatory motion with the same amplitude o ex. Water ripples • Standing Waves is a disturbance where different pints oscillate with different amplitudes, and some point may not oscillate at all o ex. Guitar string o Can only oscillate at certain discrete frequencies • Nodes are the points of a standing wave that are never displaced o More nodes = higher energy of the wave • Electrons in atoms and molecules behave like standing waves Wavefunctions and the Schrodinger Equation • A differential equation used to calculate the shape of electronic wavefunctions and their associated energies

Conditions: o Ψ(0) = Ψ(L) = 0, where 0 and L are the x-coordinates of the confining walls o Wavefunction Ψ(x) and corresponding energy E are unknowns o Equation gives infinite wavefunctions Ψ (x) and energy levels E n

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Orbitals • Orbitals are wavefunctions of individual electrons • Quantum mechanics says electrons in an atom don’t “orbit” the nucleus • An atomic orbital’s shape describes the spatial distribution of probabilities of finding the electron near various points of space • Greater the value of the square of the orbital at a particular point, Ψ (x,y,z), the greater the probability of finding the electron near that point 2

Quantum Numbers • Four are used to characterize the state of an electron in a H atom: n, l , m, m o n, l , m are orbital quantum numbers  Arise from solving schrodinger equation for H atom  Used to label the orbitals o m describes an intrinsic property of each electron called spin l

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Principle Quantum Number (n=1,2,..) • Determines energy and size of orbital • Assumes only positive integer values • Orbital’s size and energy increases as n does • A shell is formed by orbitals with the same n • Gives total number of nodes by relation: number of nodes = n - 1 Azimuthal Quantum Number (l=0,1,2,.., n-1) • aka orbital angular momentum • l describes shape of an orbital and angular momentum of an electron in that orbital • l value must be in range 0 to n-1 • Sublevels are orbitals with particular number n and l • l value 0,1,2,3 represent shapes known as sharp, principal, diffuse, and fine

Magnetic Quantum Number (m = 0, ±1, ±2,…,± l) • Describes orbital orientation with a given l relative to xyz axes • Possible m values are integers from -l, through 0, to +l o If l = 0, only m = 0 is possible, explains why s has one orbital for each n o If l = 1, m = -1,0,+1 are possible, explains why there’s three p-orbitals for each n o If l = 2, only m = -2,-1,0,+1,+2 are possible, explains the five d-orbitals for each n • Each unique n, l, m combination represents an orbital l

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• In H atoms, all orbitals with same n have same energy • Orbitals that have same energy are degenerate Spin Quantum Number (m = ±1/2) • Associated with an intrinsic angular momentum of each electron called spin • Spin is a vector that can have only two orientations with respect to identified direction: up (when m = +1/2) or down (when m = –1/2) s

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Pauli Exclusion Principle • States that no two electrons in an atom can have the same four quantum numbers • Two electrons in same orbital must have same set of n, l, and m numbers, to satisfy Pauli Exclusion the fourth, spin, must be different • If two electrons are in the same orbital, they must have opposite spins (different m ) l

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Summary • The four quantum numbers are independent of each other, but only assume specific values. The allowed values are: o n = 1, 2, 3,… o l = 0, 1, 2,…, n - 1 o m = 0, ±1, ±2,…, ± l o m = ±1/2 l

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The Shapes of Atomic Orbitals • While we use 1D wavefunction Ψ(x) to illustrate, actual wavefunction of electrons is in 3D,

Ψ(x,y,z) • An orbital is a function whose square describes how likely the electron is to be found near various points in space • Electron Density is given by the square of the orbital, and when plotted allows us to visualize the probability of finding an electron at various points • To visualize in 3D, must specify orbital by three quantum number. Generally Ψ l nlm

n=1 • At n=1, only l=0 and m =0 values are allowed, a combination that gives one orbital (1s) o Denoted as Ψ or Ψ o 1s wavefunction has shape of a sphere centred at the nucleus  Can be described using one coordinate, the radial distance r from the nucleus, because it’s spherically symmetric  Has no nodes l

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n=2 • Two types of orbitals, 2s and 2p, possible o (2,0,0) & (2,1,[-1,0, or +1]) are their respective quantum numbers ( n, l, m ) l

• 2s orbital (wavefunction Ψ or Ψ ) is also spherically symmetric o Has a node • There are three 2p orbitals, as 2p orbitals have three possible m numbers (-1,0,+1) o 2p , 2p , and 2p s o They are:  Stretched along x, y, z axes and therefore perpendicular  Degenerate (have same energy) o Correspond collectively to wavefunctions Ψ , Ψ , and Ψ o Each have one node 2s

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n=3 • Possible orbital types: 3s, 3p, and 3d o 3s and 3p shapes similar to the 2s/2p but have more nodes • 4/5 orbitals have 4 equal lobes (2+, 2-), 5th has two lobes stretched along z axis and a thick ring Note: Generally orbitals become larger has n increases, so orbitals for n=3 > n=2 > n=1 The Relative Energies of the Atomic Orbitals • Orbital energy levels are quantized — only certain energy values are allowed • In H atoms, orbital energies depend on n (the principal quantum number) o n=1 is lowest, n=2 (2s,2p0 next, then n=3 (3s,3p,3d) • Multi electron atoms, orbitals w/ same n diff. l quantum numbers, have diff. energy o For given n, lowest-highest order is s-p-d-f • Aufbau Principle states electrons occupy orbitals in the order of increasing energy

Electron Configurations • In ground state, electrons distribute themselves in a way to minimize total energy • Two common ways of writing electron configurations Full Electron Configuration • Shows number of electrons (in superscript) for each sublevel o ex. H in ground state = 1s o ex. O has 8 electrons = 1s 2s 2p 1

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Abbreviated Electron Configuration • Uses noble-gas configuration as “cores” in square brackets, followed by remaining electrons o ex. Te has 52 electrons, last noble-gas before it is Kr (36 e’s), Tc is in period 5 so the configuration is Tc: [Kr] 5s 4d 5p 2

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Valence and Core Electrons for Main Group Elements • Main-Group = column 1, 2, 13-18 • For main-group elements valence electrons are those with the highest principal • Core Electrons are those remaining in the lower-lying shells

Cations, Anions, and Isoelectronic Species • In cation formation, electrons are first removed from the highest-occupied sublevel o ex. Na (1s 2s 2p 3s ) —> Na (1s 2s 2p ) + e o ex. Ca (1s 2s 2p 3s 3p 4s ) —> Ca (1s 2s 2p 3s 3p ) + 2e • In anion formation, electrons are added to the lowest available sublevel o ex. N (1s 2s 2p ) + 3e —> N (1s 2s 2p ) o ex. Cl (1s 2s 2p 3s 3p ) + e —> Cl (1s 2s 2p 3s 3p ) 2

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Electron Configuration if Transition Metal Cations • 4s has slightly lower energy than 3d • If both 4s and 3d contain at least one electron, 3d “sinks” below 4s • In transition metals, outermost s and d contain at least one electron, so their energy ordering is 3d < 4s • When a transition metal is ionized, electrons are removed first from the highest energy 4s then from 3d • Remember: First In, First Out Orbital Diagrams • Show how electrons are distributed within sublevels • Hund’s Rule: Electrons fill orbitals of equal energy singly, with parallel spins, and start pairing up only after all these orbitals are half-filled Exceptions: Cr and Cu • Cr is [Ar] 3d 4s , not [Ar] 3d 4s • Cu is [Ar] 3d 4s , not [Ar] 3d 4s 5

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