atomic absorption and emission of light 1889 Rydberg generalized to other H emission lines: mv r n r.53 Z ke Z = r (A) * (Z ) E n -13.6 (ev) n h p o L= mvr = n 1 ke Z E= mv - r Mosley's Law E E f n E n1 *
Experimental backdrop to atomic quantum theory development Spectroscopy (emission) prism Black body spectrum hot dense body Developed in 1800 s or diffraction grating emission or bright line spectrum hot (dilute) gas prism 11-1.1
Spectroscopy 11-1.1a
418. 434.1 486.1 656.3 364.6 n= H atom absorbs and emits specific wavelengths (energies) of light n λ=(364.56) : n=3,4,5,6,..., n - 1885 Balmer: visible light n=6 Emission spectrum Red Balmer Line in Orion Nenula Absorption spectrum 11-1.
1889 Rydberg generalized to other H emission lines: Energy (discrete set) levels of H (all atoms) are unique photons absorbed /emitted unique finger print of atom 1 1 1 H - : n n n1 n 1 specifically n = n 1 +1, n 1 +, H is the Rydberg constant ( H = 10,973,731.534 m -1 ). visible Energy discrete set of H emission lines are unique (and incredibly precise) finger print of H- atom 11-1.3
He discovered in solar flash spectrum at solar eclipse ~ 1850 long before identified on Earth Other unique atomic spectra fingerprints 11-1.4
Spectroscopy (absorption) spectrometer spectrometer black body spectrum of bulb absorption lines of gas black body spectrum of bulb 11-1.5
absorption lines in Sun s spectrum 11-1.6
absorption lines in spectra of stars with different surface temperatures (mass) 11-1.6a
Before 1913 mountains of incredibly precise atomic spectral data. Atoms interact with light in highly organized discrete ways. Only some wavelengths fit. Totally un-understandable in classical physics of particles. 1913 Bohr ( something stinks in Denmark ) 11-1.7
1913 Bohr Atom v e- Classical first step Circular orbit F Ze + F= mv F= r k(e)(ze) r circular motion Coulombs Law mv r mv = ke Z r = ke Z r 1 11-1.8
v e- 1913 Bohr Atom F Ze + Circular orbit L= mvr = n ke Z 1 mv = r Angular Momentum Quantized!! into 1 n mr m ( ) = ke Z r n v = mr (Bohr had to assume this!) h = π Only quantized orbits allowed!! 0 n -10 n r n=n ( )= [.53(10) m]=[.53a ] r ke Zm Z Z 11-1.8a Angular Momentum conserved in classical problem J. Hand correction n mr =ke Z "stationary state can't change continuously r n =n ( ) ke Zm Bohr radius 1 Å = atomic size n
Bohr Atom (continued: Energy) 1 Ke Z Ke Z 1 Ke Z E= ( ) - =- r r r 1 ke Z E=n 1 ke Z E=KE+PE= mv - r ke Zm k e Z m 1 Z E =-( ) =-(13.6 ev) n n 4 n -18 for Z=1 H E 1=-.17(10) J=-13.6eV recall ke Z 1 mv = r But recall n r =n ( ) ke Zm quantized orbits quantized energy! 11- M. Shakhnovich correction
Planck s law + Einstein photons= light has some particle like properties 1901 1905 PE effect GP Thompson -1930 electron has some wave properties Point source coherent light 0. mm aperture e - beam through Crystal lattice of Be polycrystalline material De Broglie (194) matter waves m v p=mv p h 11-3
De Broglie (194) matter waves m v p=mv p h Recall Bohr said for e - in atomic orbit: h L= mvr = pr = n π h if p= λ h then r =n λ π r = nλ h π Like standing waves on a circular orbit. 11-4
Bohr Theory atomic emission spectra Z E 13 6 n. n 13.6eV { } hc (13.6)(1.6) 10 (6.66)(3) 10.973(10) 6 1 1 1 1 { R}[ ] n n 1 13.6 1.6(10) 19834 1 Z=atomic # -19 J c c 6.66(10) Js 3(10) m R 34 8 m m s Rydberg formula from Bohr!!! Z=1 hydrogen hf E E n n1 e - Electron drops down n 1 photon emitted 1 1 E E (13.6)[ ] fh n n1 n1 n c c f f h= h c 1 1 h (13.6)[ ] n n 1 1 (13.6) 1 1 { }[ ] hc n n 1 ( H = 10,973,731.534 m -1 ). Precision of R unparalleled in history of physics!!! n f 11-5
11-6
11-7
Energy (discrete set) levels of H (all atoms) are unique photons absorbed /emitted unique finger print of atom 1889 Rydberg generalized to other H emission lines: visible famous red Balmer line 11-8 1 1 1 H - : n n n1 n 1 specifically n = n 1 +1, n 1 +, H is the Rydberg constant ( H = 10,973,731.534 m -1 ). Orion UV
0 r =[.53A] n n H 1 E =-(13.6 ev) n 0eV n n=big n=4 n=3 n= n=1 + First step in energy the biggest Balmer Paschen in UV 11-9
Roentgen 1895 X-rays (X-Strallung) X-Rays and X-Ray Emission Max von Laue diffraction 191-1913 (diffraction from planes of atoms in crystal) Barkla 1911 x-ray emission hardness = penetrating power hard & soft x-rays different targets differing x-ray hardness emitted (gave us K, L, M, N x-ray emission lines) Bragg 191/13 x-ray diffraction n=dsin() [can use to measure interatomic distances d in solids!!!!] Mosely (demonstrator in Rutherford s lab at Manchester) - Bohr visits Rutherford Mosely told of new Atomic theory 1913- Mosely used Bragg reflection to determine of x-ray emission of various elements n=dsin()--- know d of crystal measure to determine 1913- Mosely s Law 1/= K [Z-] K =1 L =1 Z=atomic number!!!!! Mosely and the Numbering of the Elements - by Jaffe Doubleday NY 1971 1915 - Mosely- killed in WWI Dardanelles Campaign- (against Turkey) {Winston Churchhill s idea (1 st Lord of the Admiralty) blood bath and WC didn t come back till WWII} 11-10 mos1
Z * X-ray in n= n=1 effective charge including photo-ejected e - out n=1 hole n= e - fills n=1hole screening Atomic No.-1 n= hole K X-ray out 13.6 Z photon energy Ef hf E E f n E n1 13.6 Z 1 * E f E f 10. Z * {ev} E f (K-edge) 10. (Z-1) {ev}. * * h c λ {ev} Z * (Z -1) Z Atomic No. E f (K-edge) 0.10 (Z-1) {kev} 11-1 mos
Actual data from previous page taken in Rutgers senior undergrad lab 11-13 13-15 mos3
~ charge distribution in atom interior r +Ze -1e -e n=1 shell electron n= shell electrons 11-14 E A Q inside surf 0 Gaussian surf. Q Ze 1e inside Q (Z 1)e inside E 4 r E (Z 1)e 4 r (Z 1)e This is why Mosley s Law worked with (Z-1)!! 0 0