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

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1 6. Electronic Structure of Atoms 6.1&6.2 The Wave nature of Light and the energy of photon 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
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 character too. Wave-like – De Brogie’s matter waves: λ =h/mv Where λ -wavelength; h-planck’s constant = 6.626x10 -34 J.s; m-mass; v-speed E.g.: the wavelength of an electron moving with a speed of 5.97x10 6 m/s and mass of 9.11x10 -31 kg: λ =h/mv= 6.626x10 -34 J.s/(9.11x10 -31 kg x 5.97x10 6 m/s) =1.22X10 -10 m=1.22Angstrom (the diameter of H is ~1Angstrom) E.g.: the wavelength of a car moving with a speed of 75MPH and mass of 1400Lb: .
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