C111_7 part 2 and some ch 8

# C111_7 part 2 and some ch 8 - Bohrs Model of the Atom...

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1. e - can only have specific (quantized) energy values 2. light is emitted as e - moves from one energy level to a lower energy level Bohr’s Model of the Atom (1913) E n = -R H ( ) 1 n 2 n (principal quantum number) = 1,2,3,… R H (Rydberg constant) = 2.18 x 10 -18 J 7.3

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E = h ν E = h ν 7.3

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Bohr’s Equation 2 n Rhc E n - = E n = energy of electron in the nth energy level of the hydrogen atom (only (+) integer values allowed)

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Calculating differences between energy levels for a particle with one electron - - = - - - = 2 2 2 2 2 1 1 1 2 1 Rhc Rhc Rhc E 2 1 ) 1 ( Rhc E - = 2 2 ) 2 ( Rhc E - = E = E final - E initial let E 1 be E final E = − 1.635 x 10 −18 J ) 75 . 0 )( / 10 998 . 2 )( 10 626 . 6 )( 10 097 . 1 ( 8 34 1 7 s m x s J x m x E - = - - note: Rhc = 2.18 x 10 −18 J; this number is used in your textbook but not identified. See pages 301-306.
Bohr’s Model of the Atom Lower values of n are closer to the nucleus Electrons closer to the nucleus have lower energy and are more stable due to strong electrostatic attraction with the nucleus. By convention: lower energy levels (closer to nucleus) have more negative values of energy. Electron with no attraction to nucleus has 0 energy value.

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How this explains line spectra When energy is added, electrons resist attraction of nucleus and move to higher n levels. Electrons are then said to be “excited” When “excited” electrons relax back to lower levels, they release the same amount of energy it took to “excite” them. This energy is released as a photon of light. Energy is conserved. Same energy absorbed as emitted.

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De Broglie (1924) reasoned that e - is both particle and wave 7.4 Photons are particles of light - “Wave - particle duality” Wavelength of a particle: λ = h / mv v = velocity of e - m = mass of e - All objects have a (DeBroglie) wavelength, but for large objects, it is not large enough to observe. Because e- have such small mass, wavelength is non-negligible.
DeBroglie Wavelengths All objects have a wavelength Large objects: wavelength too small to observe. Because e- have such small mass, wavelength is non-negligible. Electron wavelengths are observed. λ = h/mv sometimes use u instead of v Example . ..

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λ = h/mu λ = 6.63 x 10 -34 / (2.5 x 10 -3 x 15.6) λ = 1.7 x 10 -32 m = 1.7 x 10 -23 nm What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? m in kg h in J s u in (m/s) 7.4
Heisenberg Uncertainty Principle Consequence of wave/particle duality We cannot know both the energy and position of an e- at the same time.

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## This note was uploaded on 01/05/2012 for the course CHEM 111 taught by Professor Lemaster during the Fall '08 term at Boise State.

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C111_7 part 2 and some ch 8 - Bohrs Model of the Atom...

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