Early Quantum Theory and Models of the Atom

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Jordan Stevenson
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1 Early Quantum Theory and Models of the Atom

Electron Discharge tube (circa 1900 s) There is something ( cathode rays ) which is emitted by the cathode and causes glowing Unlike light, these rays are deflected by electric and magnetic fields

2 Electron Discharge tube (circa 1900 s) There is something ( cathode rays ) which is emitted by the cathode and causes glowing Unlike light, these rays are deflected by electric and magnetic fields they are made of charged particles Originally thought to be molecules or ions, but e/m measurements came out with value ~10 3 larger than for hydrogen ions Beta particles discovered later in studies of radioactive materials turned out to be the same stuff Early Quantum Theory and Models of the Atom

$(win) 1800: Young, double slit experiment Fresnel: diffraction experiments 1861:$

3 Light: Particles or Waves? 17 th century: Newton vs Huygens Newton: light is particles! (win) 1800: Young, double slit experiment Fresnel: diffraction experiments 1861: Maxwell equations light is electromagnetic waves! (win) 1900: Planck, blackbody radiation formula light is? Early Quantum Theory and Models of the Atom 3

Blackbody Radiation Blackbody = a perfect absorber glass a bad absorber (for visible light, at least) metal a bad absorber (it reflects the light) soot almost perfect absorber a good model of

4 Blackbody Radiation Blackbody = a perfect absorber glass a bad absorber (for visible light, at least) metal a bad absorber (it reflects the light) soot almost perfect absorber a good model of blackbody: a hole in a wall Perfect blackbody: all wavelengths are absorbed, nothing is reflected or goes through Perfect absorber: been heated, blackbody emits radiation of all wavelengths Early Quantum Theory and Models of the Atom 4

5 Blackbody Radiation Experimental fact (Wien s law): blackbody radiation spectrum peaks at λ max =b/t, where b= m K Classical calculation (Rayleigh and Jeans, assuming that 4 radiation is due to atomic oscillations): I ~ 1/ good for high λ, diverges at low λ (ultraviolet catastrophe) Early Quantum Theory and Models of the Atom 5

6 Planck s Quantum Hypothesis Planck proved that everything works fine if one assumes that only certain energies of oscillations are allowed E n nhf 1,,3... Planck s constant: h light comes in pieces! Js I ~ e 15 1 hc 5 kt ev s 1 Early Quantum Theory and Models of the Atom 6

7 The Photoelectric Effect Light kicks electrons out of the cathode Once emitted, electrons are attracted by the anode, and create the current A Early Quantum Theory and Models of the Atom 7 I

8 The Photoelectric Effect Forward bias: electrons reach the anode even if emitted with zero speed Reverse bias: electrons can reach the anode if their initial kinetic energy is larger than the potential energy of electric field: 1 mv ev I A 1 the current stops when mv ev max 0 A I stopping potential Early Quantum Theory and Models of the Atom 8

9 Photoelectric Effect: Classical View Classical wave theory of light: energy of light is proportional to intensity <S> S u c To kick out an electron, we would need to concentrate light energy in some volume τ S c 1 mv max ev 0 Max kinetic energy is acquired by the electron if it absorbs it all V ~ S 0?? Early Quantum Theory and Models of the Atom 9

10 Photoelectric Effect: Experiment Stopping potential does not depend on intensity Stopping potential does depend on light frequency ev 0 hf work function typical values for ϕ: 4 5 ev Planck s constant (the same as for blackbody radiation!) Early Quantum Theory and Models of the Atom 10

11 Photoelectric Effect: Interpretation Einstein: light consists of small particles (photons), each of them carrying energy E=hf=hc/λ When light hits the metal, electron gets either all of the photon energy or none photons do not have mass photons always travel with speed of light c photons carry momentum p=e/c=h/λ Early Quantum Theory and Models of the Atom 11

12 Atom: What Does It Look Like? From X-ray diffraction we know that crystals have lattice constant ~10 10 m, so that must be the order of the atom size Can t see the atom by eye: atoms are much smaller than λ of visible light! Can t do much with X-rays either how will you make a lens for X-rays? So what should we do? Scattering. Early Quantum Theory and Models of the Atom 1

Rutherford Scattering α-particles are massive (~7300 m e ), so they should ignore electrons inside the atom what was expected: relatively uniform angular distribution, depending

13 Rutherford Scattering α-particles are massive (~7300 m e ), so they should ignore electrons inside the atom what was expected: relatively uniform angular distribution, depending on atom s density what was observed: most α-particles went through undisturbed, but some reflected at very large angles (up to 180 ) Early Quantum Theory and Models of the Atom 13

14 Atom is Mostly Empty Space not good failed the alpha scattering experiment Early Quantum Theory and Models of the Atom 14

15 Planetary Atom Model Problems: according to EM theory, bending charge radiates EM waves, so electrons would lose their energy and fall onto the nucleus real quick atoms show sharp spectral lines, like electrons can t radiate an arbitrary amount of energy Early Quantum Theory and Models of the Atom 15

16 Bohr s Atom Model Coulomb s law and energy conservation are OK Electrons can only exist at certain orbits (=energy levels) and do so without radiating energy Emission/absorption occurs when electron makes a transition between two stationary states: hf=e i -E f The angular momentum is quantized Early Quantum Theory and Models of the Atom 16

17 Angular Momentum Quantization Bohr s hypothesis: mvr n F electron s mass electron s speed electron s orbit radius some constant 1,,3, Coulomb s law: F k e r Centripetal force: n v r F m r kme Early Quantum Theory and Models of the Atom 17

18 Bohr Orbits r n kme What is? For the first orbit (n=1), assuming r~10 10 m, one gets ~ J s Correct answer: h Planck s constant Early Quantum Theory and Models of the Atom 18

19 Electron Energy Levels r n kme U k e r mk n e 4 n v mr K ke n mv mk e n 4 E n K U mk e n 4 Early Quantum Theory and Models of the Atom 19

20 Electron Energy Levels mk e ev E n 13.6 n ground state energy, and also ionization energy ev Rydberg constant emitted photon energy: E emitted photon wavelength: E n E n ' E R n' n hc Early Quantum Theory and Models of the Atom 0

Emission Lines Balmer series (n =) 1 1 1 R n n 3 4 5 6 7 λ, nm 656 486 434 410 397 365 It

Lyman (n =1, UV); Paschen (n =3), Bracket (n =4), Pfund (n =5 all IR) It can be seen in the

21 Emission Lines Balmer series (n =) R n n λ, nm It was discovered first because it (partially) lies in the visible spectrum Other series: Lyman (n =1, UV); Paschen (n =3), Bracket (n =4), Pfund (n =5 all IR) It can be seen in the solar spectrum, which confirms presence of hydrogen Early Quantum Theory and Models of the Atom 1

Chapter 1. From Classical to Quantum Mechanics

Chapter 1. From Classical to Quantum Mechanics Classical Mechanics (Newton): It describes the motion of a classical particle (discrete object). dp F ma, p = m = dt dx m dt F: force (N) a: acceleration