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Unformatted text preview: Molecularity Molecularity CH1010
Chapter 7 Part II Quantum Theory and Atomic Structure James P. Dittami The Particle Nature of Light The Particle Nature of Light Max Planck Albert Einstein Blackbody Radiation: Quantization of Energy Glowing objects emit only certain quantities of Energy where E = nhν Photoelectric Effect: Quantization of Light Light is particulate quantized into small bundles of electromagnetic energy or Photons Energy of a single photon: E = hν Albert Atomic Spectra Atomic Spectra Basic Idea Heat a block of iron until it glows Put energy into an object (atom) See how that energy is released Try the same with elements Light from the block is the energy released. Atomic Spectra Atomic Spectra Hydrogen Analyze light output Pass over a high energy spark Hydrogen absorbs energy gets “excited” Excess energy is released as light Consists of only specific bands of light of fixed frequency separated by black areas. Not a rainbow like light through a prism The line spectra of several elements. Absorption and Emission Absorption and Emission If e’s in H atoms are being excited and they are emitting that same energy only at specific frequencies then it follows that: Electrons absorb and emit at specific Energy levels. Again the idea of being Quantized!! The Rydberg Equation The Rydberg Equation From the data obtained with atomic spectra spectroscopists derived an equation to predict the position and wavelength of any line in a series in which λ = wavelength n1 and n2 are positive integers with n2 > n1 R is the Rydberg constant = 1.096776 x 107 m1 1 1 1 = R( 2 − 2 ) λ n1 n2 The Rydberg Equation The Rydberg Equation The Rydberg equation is based on Empirical Data not Theory Spectroscopists could predict where lines would show but could not say why. 1 1 1 = R( 2 − 2 ) λ n1 n2 The Bohr Model of the Atom The Bohr Model of the Atom Bohr Postulated the following The H atom only has certain allowable energy levels called stationary states The atom does not radiate energy while in one of its stationary states The atom changes to another stationary state by absorbing or emitting a photon whose energy matches the ΔE between the states The Bohr Model of the Atom The Bohr Model of the Atom Spectral lines result when a photon of specific energy is emitted as an electron drops from a higher E state to a lower one Bohr’s model assigns quantum numbers 1,2,3 etc. to the radius of an electrons orbit. The lower the number n, the lower the Energy Electrons in the n =1 orbit are said to be in the Ground State Electrons in n>1 orbits are said to be in an Excited State Quantum staircase. The Bohr explanation of the three series of spectral lines. Bohr’s Contribution Bohr’s Contribution Bohr derived an equation for calculating energy levels of an atom based on classical principles of electrostatic attraction and circular motion. E = −2.18 x10 −18 Z J( 2 ) n 2 Bohr’s Model Bohr’s Model From the equation for predicting the energy levels of an atom Bohr was able to derive a theoretical formula to predict the spectral lines for the H atom His matched the Rydberg formula differing in the value for the constant only by 0.05 % Limitations to the Bohr Model Limitations to the Bohr Model Accounts for spectral lines of only one electron systems H, He+, Li2+ etc. Does not work for more complicated systems We don’t use his idea of electrons in fixed orbits We still refer to “ground” and “excited states” De Broglie Wave vs. Particle De Broglie Wave vs. Particle Bohr’s work supports that Energy has a particle like nature absorption and emission occurs in fixed amounts Conclude Energy is particle like De Broglie asked can matter be wavelike? De Broglie Wave vs. Particle De Broglie Wave vs. Particle Fixed energy levels imply fixed packets. Ephoton=hν = hc/λ Recall Einstein’s derivation E=mc2 So photons have mass m=E/c2 And it follows that m=h/λ c De Broglie m=h/λ u where u is speed of an object Matter acts like it moves in a wave Restricted energies and motions Restricted energies and motions What accounts for the restricted energies Consider standing waves Affix a rope to the wall Initiate a wave like motion Only certain vibrational frequencies and wavelengths are possible. WaveGenerating Apparatus WaveGenerating Apparatus A Standing Wave A. Standing wave Guitar String fixed at each end. So only whole number multiples of λ/2 are allowed. B. Electrons in a circular orbit Only certain whole number multiples of λ are allowed which do not lead to a destructive interference. Electrons and Standing Waves Electrons and Standing Waves Electrons can be wavelike and restricted to orbits of fixed radii around nucleus Heisenberg’s Uncertainty Principle Heisenberg’s Uncertainty Principle Particles have definite location Waves are spread out in space If electrons are both particle and wavelike what can we say about their position? Conclusion: It is impossible to know the exact position and momentum (m x v) at any given instant. Uncertainty Principle Uncertainty Principle We cannot know position and speed of e Thus we cannot assign fixed paths or trajectories for the electrons orbits We can only talk about the probability of finding an electron somewhere This leaves us with the idea of orbitals the areas around the nucleus where we are likely to see the electron ...
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