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

3. Physics 102: Lecture 24, Slide 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…

4. Physics 102: Lecture 24, Slide 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):

5. Physics 102: Lecture 24, Slide 4 Preflight 24.1 If the electron in the hydrogen atom was 207 times heavier (a muon), the Bohr radius would be 1)207 Times Larger 2)Same Size 3)207 Times Smaller (Z =1 for hydrogen) Bohr radius

6. Physics 102: Lecture 24, Slide 5 Preflight 24.1 If the electron in the hydrogen atom was 207 times heavier (a muon), the Bohr radius would be 1)207 Times Larger 2)Same Size 3)207 Times Smaller Bohr radius This “m” is electron mass, not proton mass!

7. Physics 102: Lecture 24, Slide 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)

8. Physics 102: Lecture 24, Slide 7 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) 3 2 /1 = 9 Note: This is LOWER energy since negative!

9. Physics 102: Lecture 24, Slide 8 Transitions + Energy Conservation Each orbit has a specific energy: | E 1 – E 2 | = h f = h c / Photon emitted when electron jumps from high energy to low energy orbit. Photon absorbed when electron jumps from low energy to high energy:

10. Physics 102: Lecture 24, Slide 9 Transitions + Energy Conservation Each orbit has a specific energy: JAVA E n = -13.6 Z 2 /n 2 | E 1 – E 2 | = h f = h c / Photon emitted when electron jumps from high energy to low energy orbit. Photon absorbed when electron jumps from low energy to high energy:

11. Physics 102: Lecture 24, Slide 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. Which lamp is Hydrogen? Better yet… Wavelengths can be predicted! This is how neon signs work!

12. Physics 102: Lecture 24, Slide 11 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? n=2 n=3 n=1 Photon A Photon B A B

13. Physics 102: Lecture 24, Slide 12 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? n=2 n=3 n=1 Photon A Photon B A B

14. Physics 102: Lecture 24, Slide 13 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). n=2 n=3 n=1 Spectral Line Wavelengths

15. Physics 102: Lecture 24, Slide 14 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). n=2 n=3 n=1 Spectral Line Wavelengths E 1 = -13.6 eV E 2 = -3.4 eV

16. Physics 102: Lecture 24, Slide 15 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. ACT: Spectral Line Wavelengths n=2 n=3 n=1  32 < 21  32 = 21  32 > 21

17. Physics 102: Lecture 24, Slide 16 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. ACT: Spectral Line Wavelengths n=2 n=3 n=1 E 32 21  32 < 21  32 = 21  32 > 21

18. Physics 102: Lecture 24, Slide 17 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? n=2 n=3 n=1 (1)(2)(3) (4)(5)(6)

19. Physics 102: Lecture 24, Slide 18 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? n=2 n=3 n=1 (1)(2)(3) (4)(5)(6)

20. Physics 102: Lecture 24, Slide 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

21. Physics 102: Lecture 24, Slide 20 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 Would know momentum

22. Physics 102: Lecture 24, Slide 21 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) m l = component of l (- l < m l < l ) m s = spin (-½, +½) Coming Soon!

23. Physics 102: Lecture 24, Slide 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).

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

25. Physics 102: Lecture 24, Slide 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

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

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

28. Physics 102: Lecture 24, Slide 27 Usein Substitute for r n in Bohr’s Derivation 2 “Bohr radius” Note: r n has Z E n has Z 2

29. Physics 102: Lecture 24, Slide 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!

30. Physics 102: Lecture 24, Slide 29 The smaller space you try to confine a particle, the more energy it takes. –Small space => small  x –Small  x => large  p –Large  p => large KE... Let’s try it! Electric Potential Energy Electron’s Kinetic Energy Substitute into KE formula: R (nm) U (eV) KEU+KE.0053.053-27.2+13.6-13.6.53 RUKEU+KE.0053.053-27.2.53 Note:and

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