Lecture6 - 6. Electronic Structure of Atoms 6.1&6.2 The...

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1 6. Electronic Structure of Atoms What is light? – Light is an electromagnetic wave: Wavelength: λ (SI unit: length) Frequency: ν (Hz) Speed of light: c (c=299,792,458 m / s in vacuum) c= λ ν . The electromagnetic spectrum
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2 – Light consists of particles – photons Energy of photon: E=h ν Where: h-planck’s constant h=6.626 x 10 -34 J.s; v -frequency of photon. • Example: Calculate the visible photon: – Violet λ =400nm: E=h ν =hc/ λ =6.626 x 10 -34 J.s x (3 x10 8 m/s)/(400x10 -9 m)=4.97x10 -19 J/photon => 4.97x10 -19 J/photon x(6.022x10 23 photon/mol)=2.99x10 5 J/mol – Red λ =750nm: E=h ν =hc/ λ =6.626 x 10 -34 J.s x (3 x10 8 m/s)/(750x10 -9 m)=2.65x10 -19 J/photon = >2.65x10 -19 J/photon x(6.022x10 23 photon/mol)=1.60x10 5 J/mol 6.5 Quantum Mechanics and Atomic Orbitals • Line spectrum of hydrogen atom: Line spectrum: a spectrum containing radiation of only specific wavelengths. Rydberg equation: 1/ λ =(R H )(1/n 1 2 - 1/n 2 2 ) Where R H is the Rydberg constant (R H =1.096776 x 10 7 m -1 ), and n 1 and n 2 are positive integers. (n 1 < n 2 ) 410nm: 4.85x10 -19 J/photon; n 1 =2 n 2 =6 434nm: 4.58x10 -19 J/photon; n 1 =2 n 2 =5 486nm: 4.09x10 -19 J/photon; n 1 =2 n 2 =4 656nm: 3.03x10 -19 J/photon; n 1 =2 n 2 =3
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3 • Bohr’s Model: Three postulates of Bohr’s Model: – Only orbits of certain radii, corresponding to certain definite energies, are permitted for the electron in a hydrogen atom. – An electron in a permitted orbit has a specific energy and is in an “allowed” energy state. An electron in an allowed energy state will not radiate energy and therefore will not spiral into the nucleus. – Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy state to another. This energy is emitted or absorbed as a photon, *Limitations of the Bohr Model: Only explain the line spectra of hydrogen atom or one-electron ions. – Energy for orbit: Where n = integer. – Energy of photon during emission or absorption: . 2 18 2 10 18 . 2 n J n hcR E H - × - = - = - - = = - × - = - - = - 2 1 2 2 2 1 2 2 18 2 1 2 2 1 1 1 1 1 10 18 . 2 1 1 n n R hc E n n J n n hcR E H H λ
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4 5.45E-19 (365nm) 4.84E-19 (410nm) 4.58E-19 (434nm) 4.09E-19 (486nm) 3.03E-19 (656nm) E(J) (2 n 2 ) 2.42E-19 (821nm) 2.18E-18 (13.6eV; IE 1 ) 0 1.81E-19 (1096nm) 2.12E-18 (94nm) - 6.06E-21 6 1.55E-19 (1284nm) 2.09E-18 (95nm) -8.72E-21 5 1.06E-19 (1880nm) 2.04E-18 (97nm) -1.36E-20 4 1.94E-18 (103nm) -2.42E-19 3 1.64E-18 (122nm) -5.45E-19 2 -2.18E-18 1 E(J) (2 n 2 ) E(J) (1 n 2 ) E(J) n 6.4 The wave behavior of matter • Radiation has either wave-like or particle-like character depends on experimental circumstances. • All matters also have either wave-like or particle-like
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This note was uploaded on 11/06/2008 for the course CHEM 121 l taught by Professor Na during the Spring '08 term at John Brown.

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Lecture6 - 6. Electronic Structure of Atoms 6.1&amp;6.2 The...

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