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1.) Which color in the visible spectrum has the highest frequency? Which has the lowest frequency? 2.) Is the frequency of the radiation used in a microwave oven higher or lower than that from a FM radio station broadcasting at 91.7MHz? 3.) Is the wavelength of x-rays longer or shorter than that of ultraviolet light?

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Traditional Theories: Intensity of radiation should increase continuously with decreasing wavelength

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Lead to the discovery of a quantum … which is like a packet of energy released when there is a transfer. Vibrations in atoms are quantized (i.e. Only certain vibrations with certain frequencies are allowed)

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Assumption: Energy is carried on the amplitude of a wave (as in classical waves). Prediction: Since the amplitude of an EM wave correlates with the brightness of the light, light of high enough intensity irradiating a metal for a long enough period of time should be able to eject electrons from the surface of a metal. Reality: It was the frequency of the light that determined whether or not electrons were ejected regardless of the time of irradiation. The brightness (amplitude) only determined how many were ejected per unit time once ejection started occurring.

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Einstein (1905) incorporated Planck’s equation with the idea that light had (mass-less) particle properties (photon). These photons are “packets” of energy where E depends on the frequency of the photon (E = hν).

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A 60W, monochromatic laser beam gives off photons of wavelength 650nm. How long does it take for 2.5moles of these photons to be given off? Answer: E = hc/λ = (6.626x10 -34 Js)(3.0x10 8 m/s)/6.50x10 -7 m = 3.06x10 -19 J/photon (3.06x10 -19 J/photon)(6.022x10 23 photons/mol)(2.5mol) = 4.60x10 5 J 4.60x10 5 J / (60J/s) = 7673.4s /(3600s/1hr) = 2.13h

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Compare the energy of a mole of photons of orange light (625nm) with the energy of a mole of photons of microwave radiation having a frequency of 2.45GHz (1GHz = 109s -1 ). Which has the greater energy? By what factor is one greater than the other? Answer: E = (6.626x10 -34 Js)(3.00x10 8 m/s)/(6.25x10 -7 m) = 3.18x10 -19 J 3.18x10 -19 J(6.022x10 23 ) = 1.92x10 5 J/mol E = (6.626x10 -34 Js)(2.45x10 9 Hz) = 1.623x10 -24 J 1.623x10 -24 (6.022x10 23 ) = 9.78x10 -1 J/mol 1.9x10 5 / 9.7x10 -1 = 1.96x10 5

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Atomic Line Spectra Atomic Emission Spectra

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First connection between line spectra and quantum ideas of Planck and Einstein. Bohr Model: Electrons orbit the nucleus of the atom like planets going around the sun. Only certain stable orbits are allowed (quantized) to keep the electron (a charged, accelerating particle) from crashing into the nucleus.

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n is an integer equal to or greater than 1 and Rhc = 2.179x10-18J/atom or 1312kJ/mol Principle quantum number Note: Potential energy = 0 at infinity

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1) Electron in ground state 2) Electron jumps to “excited state” from absorption of outside energy (Energy absorbed = positive) 3) Electron transitions back down giving off photon that is equal in energy to the transition down (energy emitted = negative)

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Lyman (UV), Balmer (Visible), and Paschen (IR), series of the hydrogen atom.

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Calculate the energy of the n=3 state of the H atom in a) joules per atom and b) kilojoules per mole. Rhc = 2.179x10-18J/atom or 1312kJ/mol Answer: E = -Rhc/n2 = -2.179x10-18J/atom / 32 = -2.421x10-19J E = -1312kJ/mol / 32 = -145.8kJ/mol

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Each electron in an atom has a unique set of 4 quantum numbers which describe it. Principal quantum number Angular momentum quantum number Magnetic quantum number Spin quantum number

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Pauli Exclusion Principle No two electrons in an atom can have the same four quantum numbers. Wolfgang Pauli

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Principal Quantum Number Generally symbolized by n, it denotes the shell (energy level) in which the electron is located. Number of electrons that can fit in a shell: 2n 2

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Angular Momentum Quantum Number The angular momentum quantum number, generally symbolized by l, denotes the orbital (subshell) in which the electron is located.

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Magnetic Quantum Number The magnetic quantum number, generally symbolized by m l, denotes the orientation of the electron’s orbital with respect to the three axes in space.

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Assigning the Numbers The three quantum numbers (n, l, and m l ) are integers. The principal quantum number (n) cannot be zero 1, 2, 3, etc. The angular momentum quantum number (l ) can be any integer between 0 and n - 1. For n = 3, l can be either 0, 1, or 2. The magnetic quantum number (m l ) can be any integer between -l and +l. For l = 2, m can be either -2, -1, 0, +1, +2.

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Spin Quantum Number Spin quantum number (m s ) denotes the behavior (direction of spin) of an electron within a magnetic field. Possibilities for electron spin:

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An orbital is a region within an atom where there is a probability of finding an electron. This is a probability diagram for the s orbital in the first energy level… Orbital shapes are defined as the surface that contains 90% of the total electron probability.

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Schrodinger Wave Equation probability Equation for probability of a single electron being found along a single axis (x-axis) Erwin Schrodinger

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Heisenberg Uncertainty Principle You can find out where the electron is, but not where it is going. OR… You can find out where the electron is going, but not where it is! “One cannot simultaneously determine both the position and momentum of an electron.” Werner Heisenberg

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Orbitals of the same shape (s, for instance) grow larger as n increases Nodes are regions of low probability within an orbital.

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The s orbital has a spherical shape centered around the origin of the three axes in space. s orbital shape

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P orbital shape

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Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of: …and a “dumbell with a donut”! “double dumbells” d shaped orbitals

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Shape of f orbitals

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Orbital filling table

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[He]2s 2 p 6 ____ ____ ____ ____ ____ 1s 2s 2p 1s 2 2s 2 p 6 Neon [He]2s 2 p 5 ____ ____ ____ ____ ____ 1s 2s 2p 1s 2 2s 2 p 5 Fluorine [He]2s 2 p 4 ____ ____ ____ ____ ____ 1s 2s 2p 1s 2 2s 2 p 4 Oxygen [He]2s 2 p 3 ____ ____ ____ ____ ____ 1s 2s 2p 1s 2 2s 2 p 3 Nitrogen [He]2s 2 p 2 ____ ____ ____ ____ ____ 1s 2s 2p 1s 2 2s 2 p 2 Carbon [He]2s 2 p 1 ____ ____ ____ ____ ____ 1s 2s 2p 1s 2 2s 2 p 1 Boron [He]2s 2 ____ ____ ____ ____ ____ 1s 2s 2p 1s 2 2s 2 Beryllium [He]2s 1 ____ ____ ____ ____ ____ 1s 2s 2p 1s 2 2s 1 Lithium Noble gas notation Orbital notationConfiguration notation Element

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Irregular confirmations of Cr and Cu Chromium steals a 4s electron to half fill its 3d sublevel Copper steals a 4s electron to FILL its 3d sublevel

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Half of the distance between nuclei in covalently bonded diatomic molecule "covalent atomic radii" Periodic Trends in Atomic Radius Radius decreases across a period Increased effective nuclear charge due to decreased shielding Radius increases down a group Addition of principal quantum levels Determination of Atomic Radius

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Table of Atomic Radii

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Tends to increase across a period Electrons in the same quantum level do not shield as effectively as electrons in inner levels Irregularities at half filled and filled sublevels due to extra repulsion of electrons paired in orbitals, making them easier to remove Tends to decrease down a group Outer electrons are farther from the nucleus Ionization Energy: the energy required to remove an electron from an atom

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Mg + 738 kJ Mg + + e - Mg + + 1451 kJ Mg 2+ + e - Mg 2+ + 7733 kJ Mg 3+ + e - Ionization of Magnesium

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Table of 1st Ionization Energies

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Electron Affinity is the energy change associated with the addition of an electron. So … think the opposite of ionization energy. 1.) Electron affinity tends to increase across a period. 2.) Affinity tends to decrease as you go down in a group. Electrons farther from the nucleus experience less nuclear attraction Some irregularities due to repulsive forces in the relatively small p orbitals

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Table of Electron Affinities

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Electronegativity is a measure of the ability of an atom in a chemical compound to attract electrons. Trend …. 1.) Electronegativity tends to increase as you go across a period. 2.) Electronegativity tends to decrease as you go down a group or remain the same.

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When you subtract the electronegativity values of two atoms bound together … you use the value to determine what kind of bond you have. Non-polar covalent= 0-0.3 Polar Covalent Bonds= 0.3- 1.7 Ionic Bonds= 1.7- 3.3

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Periodic Table of Electronegativities

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Cations Positively charged ions Smaller than the corresponding atom Anions Negatively charged ions Larger than the corresponding atom Ionic Radii

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Table of Ion Sizes

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Summary of Periodic Trends

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