Physics 1030 General Physics II

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1 Final Exam April 20 6:00-9:00 pm University Center, Rm (seats 1-211) Phys 1030 General Physics II (Gericke) 1

2 The De Broglie Wavelength (Section 29.5) de Broglie wavelength: hp Wavelength for a particle. h J s Non-relativistic h mv h 2mKE is very small Wavelength inversely proportional to mass of particle Phys 1030 General Physics II (Gericke) 2

Initially random pattern of hits slowly builds up interference pattern.

to hit the screen at various locations. From A. Tonomura, J. Endo, T.

3 The De Broglie Wavelength (Section 29.5) Double slit experiment: electrons Electrons hit screen one at a time. Initially random pattern of hits slowly builds up interference pattern. The wave associated with an electron gives the probability for the electron to hit the screen at various locations. From A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Ezawa Am. J. Phys. 57 (2): 117, Feb Phys 1030 General Physics II (Gericke) 3

4 The Heisenberg Uncertainty Principle (Section 29.6) The Heisenberg Uncertainty Principle Diffraction with electrons: Electrons with momentum p x pass through slit. Diffraction pattern: some electrons acquired momentum in y direction, up to Δp y. 1st dark fringe: sin W Phys 1030 General Physics II (Gericke) 4

5 The Heisenberg Uncertainty Principle (Section 29.6) for small θ, de Broglie: py tan sin W p tan sin px h x py p W h y h W Phys 1030 General Physics II (Gericke) 5

6 The Heisenberg Uncertainty Principle (Section 29.6) The principle applies separately to any component of momentum and position: And to energy and time h 4 h x 4 p y y p x E t h Phys 1030 General Physics II (Gericke) 6

7 The Heisenberg Uncertainty Principle (Section 29.6) C&J (9 th ) An object is moving along a straight line, and the uncertainty in its position is 2.5 m. (a) Find the minimum uncertainty in the momentum of the object. Find the minimum uncertainty in the object's velocity, assuming that the object is (b) a golf ball (mass kg) and (c) an electron Phys 1030 General Physics II (Gericke) 7

8 The Heisenberg Uncertainty Principle (Section 29.6) A subatomic particle created in an experiment exists in a certain state for a time of Δt = 7.4 x s before decaying into other particles. Apply both the Heisenberg uncertainty principle and the equivalence of energy and mass (see Section 28.6) to determine the minimum uncertainty involved in measuring the mass of this short-lived particle Phys 1030 General Physics II (Gericke) 8

9 The Nature of the Atom (Chapter 30) Rutherford and the Discovery of the Nucleus (Section 30.1) Phys 1030 General Physics II (Gericke) 9

to investigate the properties of (Gold) atoms. In the Thompson model of the atom, one would expect the s to be scattered uniformly and at small angles.

10 Rutherford and the Discovery of the Nucleus (Section 30.1) Discovery of the atomic nucleus (Rutherford, 1908 Nobel Prize in Chemistry but not for this work) Rutherford accelerated ionized helium atoms ( particles) at a Gold foil to investigate the properties of (Gold) atoms. In the Thompson model of the atom, one would expect the s to be scattered uniformly and at small angles. However, Rutherford found that most of them were not deflected at all and some of them were scattered at large angles (some backward), which was consistent with something very hard, heavy and very small located somewhere inside the atom: The atomic nucleus! Phys 1030 General Physics II (Gericke) 10

11 Rutherford and the Discovery of the Nucleus (Section 30.1) Early model (Thompson s plum pudding): positive pudding, negative plums (electrons). Rutherford scattering contradicted plum pudding model. alpha particles scattering on thin gold foil. Most pass straight through, 1 in ~20,000 scattered by Phys 1030 General Physics II (Gericke) 11

12 Rutherford and the Discovery of the Nucleus (Section 30.1) Incorrect Planetary Model: negative electron positive nucleus Phys 1030 General Physics II (Gericke) 12

Line Spectra (Section 30.2) Atomic Spectra Light emission from gas discharge: Atoms are excited electrically, and emit light at characteristic wavelengths.

13 Line Spectra (Section 30.2) Atomic Spectra Light emission from gas discharge: Atoms are excited electrically, and emit light at characteristic wavelengths. Bruce Nauman Human/Need/Desire Museum of Modern Art, NYC Discrete wavelengths observed for simple systems Phys 1030 General Physics II (Gericke) 13

14 Line Spectra (Section 30.2) The Hydrogen Spectrum simplest atom, should be simple to describe and understand. Balmer discovered a pattern in the spectrum of the H atom: more spectral series found in the infrared Phys 1030 General Physics II (Gericke) 14

15 Line Spectra (Section 30.2) The Hydrogen Spectrum Phys 1030 General Physics II (Gericke) 15

16 Line Spectra (Section 30.2) The Hydrogen Spectrum Lyman Series Balmer series 1 1 R 1 ; 2 n n 2,3, R ; 2 4 n n 3, 4,5, Paschen series R ; n 4,5,6, 2 9 n Phys 1030 General Physics II (Gericke) 16

17 Line Spectra (Section 30.2) The Hydrogen Spectrum Rydberg formula: R n 1 n 2 n 1,2,3, ; n n 1, n 2, n 3, Rydberg constant: 7-1 R m Phys 1030 General Physics II (Gericke) 17

Physics 1C. Modern Physics Lecture

Physics 1C. Modern Physics Lecture Physics 1C Modern Physics Lecture "I ask you to look both ways. For the road to a knowledge of the stars leads through the atom; and important knowledge of the atom has been reached through the stars."