MSE 321 Structural Characterization

Size: px

Start display at page:

Download "MSE 321 Structural Characterization"

Edmund Pitts
5 years ago
Views:

1 r lim = 0 r e + e - mv 2/r e 2 /(4πε 0 r 2 ) KE } W = ½mv 2 - Electrons e =.6022x0-9 C ε 0 = 8.854x0-2 F/m m 0 = 9.094x0-3 kg PE } e 2 4πε 0 r (PE= F d ) e e W = - =( 2 2 -e 2 8πε 0 r 4πε 0 r ) mv 2 e 2 = r 4πε 0 r 2 (always negative) 8πε 0 r } e v = 2 4πε 0 rm ½mv 2 = e 2 8πε 0 r The electron is bound to the nucleus by the positive energy W. But this model would continuously radiate energy and so be unstable! Bohr suggested that electrons can only lose energy of a certain size only orbits where L = nh/2π are stable. mvr = nh 2π n =, 2, 3 v = nh 2πrm -e πme W = ( 2 2 8πε ε 0 h 2 0 )( n) 2 Niels Henrik David Bohr ( ) = -me 4 8ε 2 h 2 0 e = 2 r 4πε 0 rm n = ε 0 h n πme 2 Å 2n2 n n 2 ev n = 3.6 ev binding energy n = ev binding energy (n determines energy) Electronic transitions are quantised: hν = W n2 W n h = 6.626x0-34 Js (Planck s constant) ( ev =.6022x0-9 J) Hydrogen Spectral Lines (UV) Rydberg Formula: Rydberg Constant: 8 (IR) e =.6022x0-9 C ε 0 = 8.854x0-2 F/m m 0 = 9.094x0-3 kg h = 6.626x0-34 Js

Quantum Numbers Principal quantum number, n n =, 2, 3 (K, L, M ) energy shell n = 2 n = Orbital quantum number, l

diffuse l = 3: fundamental orbital angular momentum = {l (l + )} ½ h Charles Barkla 877-944 Magnetic quantum

angular momentum quantum number, j j = l ± s l s j l + s Total angular momentum = { j ( j + )} ½ h Aufbau Principle

2 Quantum Numbers Principal quantum number, n n =, 2, 3 (K, L, M ) energy shell n = 2 n = Orbital quantum number, l AKA azimuthal, orbital, or angular-momentum quantum number l = 0,, 2 (n ) l = 0: sharp l = : principal l = 2: diffuse l = 3: fundamental orbital angular momentum = {l (l + )} ½ h Charles Barkla Magnetic quantum number, m l -l m l +l Mg Spin quantum number, s s = ±½ intrinsic angular momentum Total Angular Momentum Total angular momentum quantum number, j j = l ± s l s j l + s Total angular momentum = { j ( j + )} ½ h Aufbau Principle Orbitals fill in order of increasing n + l Where two orbitals have the same value of n + l, they are filled in order of increasing n

Notation spdf IUPAC n l m l s j Siegbahn s K 0 0 ±½ ½ 2s L 2 0 0 ±½ ½ 2p L 2 2 0 ±½ ½ 2p L 3 2 ± ±½ 3 3s M 3 0 0 ±½ ½ 3p M 2 3 0 ±½ ½ 3p M 3

6 4 3 0, ±2 ±½ 5 4f N 7 4 3 ±, ±3 ±½ 7 MSE 42/52 Introduction to Electron Microscopy =m l (max) +½ s 2s 2p /2 2p 3/2 3s 3p /2 3p 3/2 3d 3/2

3 Notation spdf IUPAC n l m l s j Siegbahn s K 0 0 ±½ ½ 2s L ±½ ½ 2p L ±½ ½ 2p L 3 2 ± ±½ 3 3s M ±½ ½ 3p M ±½ ½ 3p M 3 3 ± ±½ 3 3d M ± ±½ 3 3d M , ±2 ±½ 5 4s N ±½ ½ 4p N ±½ ½ 4p N 3 4 ± ±½ 3 4d N ± ±½ 3 4d N , ±2 ±½ 5 4f N , ±2 ±½ 5 4f N ±, ±3 ±½ 7 MSE 42/52 Introduction to Electron Microscopy =m l (max) +½ s 2s 2p /2 2p 3/2 3s 3p /2 3p 3/2 3d 3/2 3d 5/2 4s 4p /2 4p 3/2 4d 3/2 4d 5/2 4f 5/2 4f 7/2 Rules:. n < 0 2. l = ± 3. m l = 0 or ± Electron Transitions Karl Manne Georg Siegbahn

4 Electron Transitions Rules:. n < 0 2. l = ± 3. m l = 0 or ± Karl Manne Georg Siegbahn Elastic Scattering Reflection Refraction Rayleigh Scattering Thomson Scattering

5 Thomson Scattering elastic scattering of EM radiation by a free charged particle r 2θ µ 0 = 4πx0-7 mkg/c 2 e =.6022x0-9 C m = 9.094x0-3 kg K = 7.94x0-30 m 2 2θ = angle between incident and scattered photon. The scattered wave is elastic, coherent and spherical (symmetric with respect to the scattering angle, i.e., as much is scattered forwards as backwards). 2. Electrons have the same Thomson cross-section for polarized and unpolarized light. 3. The scattered radiation is polarized: 00% in the plane orthogonal to the direction of incident photon and 0% in the direction of the incident photon. 4. Thomson scattering is one of the most important processes for impeding the escape of photons through a medium. Inelastic Scattering Fluorescence Compton Scattering Raman Scattering Absorption

$Compton Scattering Incoherent no phase relationship between incident and scattered beams Useless for diffraction just adds to background Note: Thomson scattering is just the low-energy limit of$

6 Compton Scattering Incoherent no phase relationship between incident and scattered beams Useless for diffraction just adds to background Note: Thomson scattering is just the low-energy limit of Compton scattering (νh << mc 2 ) in which the electron is too tightly bound to receive momentum from the photon, so the interaction is elastic and λ = 0. Absorption Beer-Lambert Law Penetration depth/mean free path determines depth of specimen sampled Varies with wavelength and material, but typically several microns for x-rays, shorter for electrons I = I 0 exp(-µx) I = I 0 exp[-(µ/ρ)ρ x] µ = linear absorption coefficient (increases as Z increases), units of cm - µ/ρ = mass absorption coefficient, independent of physical state, units cm 2 /g ρ(pb) = 3.84 g/cm 3 For λ = 0.4 Å, µ/ρ ~ 30 cm 2 /g As λ decreases, µ/ρ decreases (photons of higher E pass more easily) When λ reduced just below the critical value ( Å for Pb), µ/ρ rises by a factor of ~ 5. K absorption edge. Photons/electrons now have sufficient energy to knock out K electrons energy converted into K fluorescent radiation. Just above K edge, 0% of I gets through 832 µm of Pb Just below K edge, 0% of I gets through just 79 µm of Pb and only % makes it through 832 µm. Absorption = scattering + true absorption (production of photoelectrons & fluorescence)

Chapter 37 Early Quantum Theory and Models of the Atom

Chapter 37 Early Quantum Theory and Models of the Atom Units of Chapter 37 37-7 Wave Nature of Matter 37-8 Electron Microscopes 37-9 Early Models of the Atom 37-10 Atomic Spectra: Key to the Structure