Bohr vs. Correct Model of Atom

1. Bohr vs. Correct Model of Atom Physics 102: Lecture 24 Today’s Lecture will cover Ch 27.6-7, 28.6 Physics 102: Lecture 24, Slide 1

2. Science fiction The Bohr model is complete nonsense. Electrons do not circle the nucleus in little planet-like orbits. The assumptions injected into the Bohr model have no basis in physical reality. BUT the model does get some of the numbers right for SIMPLE atoms… Physics 102: Lecture 24, Slide 2

3. What does work, approximately Hydrogen-like energy levels (relative to a free electron that wanders off): Typical hydrogen-like radius (1 electron, Z protons): Physics 102: Lecture 24, Slide 3

4. Bohr radius Preflight 24.1 If the electron in the hydrogen atom was 207 times heavier (a muon), the Bohr radius would be • 207 Times Larger • Same Size • 207 Times Smaller (Z =1 for hydrogen) Physics 102: Lecture 24, Slide 4

5. Bohr radius This “m” is electron mass, not proton mass! Preflight 24.1 If the electron in the hydrogen atom was 207 times heavier (a muon), the Bohr radius would be • 207 Times Larger • Same Size • 207 Times Smaller Physics 102: Lecture 24, Slide 5

6. Preflight 24.2 A single electron is orbiting around a nucleus with charge +3. What is its ground state (n=1) energy? (Recall for charge +1, E= -13.6 eV) 1) E = 9 (-13.6 eV) 2) E = 3 (-13.6 eV) 3) E = 1 (-13.6 eV) Physics 102: Lecture 24, Slide 6

7. 32/1 = 9 Preflight 24.2 A single electron is orbiting around a nucleus with charge +3. What is its ground state (n=1) energy? (Recall for charge +1, E= -13.6 eV) 1) E = 9 (-13.6 eV) 2) E = 3 (-13.6 eV) 3) E = 1 (-13.6 eV) Note: This is LOWER energy since negative! Physics 102: Lecture 24, Slide 7

8. Transitions + Energy Conservation • Each orbit has a specific energy: • Photon emitted when electron jumps from high energy to low energy orbit. Photon absorbed when electron jumps from low energy to high energy: | E1 – E2| = h f = h c / l Physics 102: Lecture 24, Slide 8

9. Transitions + Energy Conservation • Each orbit has a specific energy: En= -13.6 Z2/n2 • Photon emitted when electron jumps from high energy to low energy orbit. Photon absorbed when electron jumps from low energy to high energy: | E1 – E2| = h f = h c / l JAVA Physics 102: Lecture 24, Slide 9

10. Line Spectra In addition to the continuous blackbody spectrum, elements emit a discrete set of wavelengths which show up as lines in a diffraction grating. This is how neon signs work! Which lamp is Hydrogen? Better yet… Wavelengths can be predicted! Physics 102: Lecture 24, Slide 10

11. n=3 n=2 A B n=1 Preflight 24.3 Electron A falls from energy level n=2 to energy level n=1 (ground state), causing a photon to be emitted. Electron B falls from energy level n=3 to energy level n=1 (ground state), causing a photon to be emitted. Which photon has more energy? • Photon A • Photon B Physics 102: Lecture 24, Slide 11

12. n=3 n=2 A B n=1 Preflight 24.3 Electron A falls from energy level n=2 to energy level n=1 (ground state), causing a photon to be emitted. Electron B falls from energy level n=3 to energy level n=1 (ground state), causing a photon to be emitted. Which photon has more energy? • Photon A • Photon B Physics 102: Lecture 24, Slide 12

13. n=3 n=2 n=1 Example Spectral Line Wavelengths Calculate the wavelength of photon emitted when an electron in the hydrogen atom drops from the n=2 state to the ground state (n=1). Physics 102: Lecture 24, Slide 13

14. n=3 n=2 n=1 Example Spectral Line Wavelengths Calculate the wavelength of photon emitted when an electron in the hydrogen atom drops from the n=2 state to the ground state (n=1). E2= -3.4 eV E1= -13.6 eV Physics 102: Lecture 24, Slide 14

15. n=3 n=2 n=1 ACT: Spectral Line Wavelengths Compare the wavelength of a photon produced from a transition from n=3 to n=2 with that of a photon produced from a transition n=2 to n=1. (1) l32 < l21 (2) l32 = l21 (3) l32 > l21 Physics 102: Lecture 24, Slide 15

16. n=3 n=2 n=1 ACT: Spectral Line Wavelengths Compare the wavelength of a photon produced from a transition from n=3 to n=2 with that of a photon produced from a transition n=2 to n=1. (1) l32 < l21 (2) l32 = l21 (3) l32 > l21 E32 < E21 so l32 > l21 Physics 102: Lecture 24, Slide 16

17. n=3 n=2 n=1 Preflight 24.4 The electrons in a large group of hydrogen atoms are excited to the n=3 level. How many spectral lines will be produced? (1) (2) (3) (4) (5) (6) Physics 102: Lecture 24, Slide 17

18. n=3 n=2 n=1 Preflight 24.4 The electrons in a large group of hydrogen atoms are excited to the n=3 level. How many spectral lines will be produced? (1) (2) (3) (4) (5) (6) Physics 102: Lecture 24, Slide 18

19. Preflights 24.6, 24.8 So what keeps the electron from “sticking” to the nucleus? Centripetal Acceleration Pauli Exclusion Principle Heisenberg Uncertainty Principle To be consistent with the Heisenberg Uncertainty Principle, which of these properties can not be quantized (have the exact value known)? (more than one answer can be correct) Electron Orbital Radius Electron Energy Electron Velocity Electron Angular Momentum Physics 102: Lecture 24, Slide 19

20. Would know momentum Preflights 24.6, 24.8 So what keeps the electron from “sticking” to the nucleus? Centripetal Acceleration Pauli Exclusion Principle Heisenberg Uncertainty Principle To be consistent with the Heisenberg Uncertainty Principle, which of these properties can not be quantized (have the exact value known)? (more than one answer can be correct) Electron Orbital Radius Electron Energy Electron Velocity Electron Angular Momentum Would know location Physics 102: Lecture 24, Slide 20

21. Coming Soon! Quantum Mechanics • Predicts available energy states agreeing with Bohr. • Don’t have definite electron position, only a probability function. • Orbitals can have 0 angular momentum! • Each electron state labeled by 4 numbers: n = principal quantum number (1, 2, 3, …) l = angular momentum (0, 1, 2, … n-1) ml = component of l (-l < ml < l) ms = spin (-½ , +½) Physics 102: Lecture 24, Slide 21

22. Summary • Bohr’s Model gives accurate values for electron energy levels... • But Quantum Mechanics is needed to describe electrons in atom. • Electrons jump between states by emitting or absorbing photons of the appropriate energy. • Each state has specific energy and is labeled by 4 quantum numbers (next time). Physics 102: Lecture 24, Slide 22

23. JAVA Links • Bohr Atom • Debroglie Atom • Schroedinger Atom Physics 102: Lecture 24, Slide 23

24. Bohr’s Model • Mini Universe • Coulomb attraction produces centripetal acceleration. • This gives energy for each allowed radius. • Spectra tells you which radii orbits are allowed. • Fits show this is equivalent to constraining angular momentum L = mvr = n h JAVA DeBroglie Physics 102: Lecture 24, Slide 24

25. Bohr’s Derivation Physics 102: Lecture 24, Slide 25

26. Bohr’s Derivation 1 Circular motion Total energy Quantization of angular momentum: Physics 102: Lecture 24, Slide 26

27. Bohr’s Derivation 2 Use in “Bohr radius” Substitute for rn in Note: rn has Z En has Z2 Physics 102: Lecture 24, Slide 27

28. So Why is Bohr Wrong? • Bohr gets energy levels correct, and also approximate size. • Quantized electron velocity and radius violates Heisenberg uncertainty principle. • It is “LUCKY” that Bohr model got anything correct! Physics 102: Lecture 24, Slide 28

29. Note: and Let’s try it! The smaller space you try to confine a particle, the more energy it takes. • Small space => small D x • Small Dx => large Dp • Large Dp => large KE ... • Electric Potential Energy • Electron’s Kinetic Energy Substitute into KE formula: Physics 102: Lecture 24, Slide 29

30. See you later! • Read Textbook Section 28.7 Physics 102: Lecture 24, Slide 30