Electron tracks in a cloud chamber (1937) Physics 116 sciencemuseum.org.uk Session 37 Models of atoms Dec 1, 2011 R. J. Wilkes Email: ph116@u.washington.edu
Announcements • � Exam 3 score files posted today • � Average 77, std dev 13.5 • � Final exam is NOT droppable! Everyone must take the final. • � Final will be about 1/3 on material since exam 3, remainder covers all material discussed during the course • � As usual there will be a review session last day of term, and formula page(s?) will be posted
Lecture Schedule (to end of term) !"#$%& !"
1. When a beam of light, which is traveling in air, is reflected by a glass surface, there is " ! " " A) a 90° phase change in the reflected beam. " B) no phase change in the reflected beam. " C) a 180° phase change in the reflected beam. " D) a 60° phase change in the reflected beam. " E) a 45° phase change in the reflected beam. " Answer: C " Phase change � = 180° for reflection off a higher index medium. " 2. A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the slit width is doubled? " A) It will be cut to one-quarter its original size. " B) It will be cut in half. " C) It will double. " D) It will become four times as large. " E) It will become eight times as large. " Answer: B " 3. Light of wavelength 687 nm is incident on a single slit 0.75 mm wide. At what distance from the slit should a screen be placed if the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the screen? " A) 0.39 m " B) 0.93 m " C) 1.1 m " D) 1.5 m " E) 1.9 m " Answer: B "
4. A puddle of water has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the indices of refraction of gasoline and water are 1.40 and 1.33, respectively, what is the minimum thickness of the film to see a bright reflection? " A) 100 nm " B) 200 nm " C) 300 nm " D) 400 nm " E) 500 nm n= 1.40 " Answer: A (see Figure 28-14 and related discussion in textbook) 5. A certain astronomical telescope has a diameter of 5.60 m. What is the minimum angle of resolution for this telescope at a wavelength of 620 nm? " A) 1.11 � 10-7 rad " B) 3.11 � 10-7 rad " C) 2.70 � 10-7 rad " D) 1.35 � 10-7 rad " E) 4.05 � 10-7 rad " Answer: D "
6. Which one of the following statements is false? " A) The laws of physics are the same in all inertial frames of reference. " B) Observers in different inertial frames can disagree about the location of an event. " C) Observers in different inertial frames can disagree about the time separating two events. " D) Einstein's theory of special relativity applies to accelerated frames of reference. " E) Relativistic time dilation does apply to biological processes. " Answer: D (special relativity is for inertial frames; general relativity covers accelerated frames) " 7. Observer A sees a ruler moving by in a relativistic train and measures its length to be L A. Observer B moves together with the train and measures the length of the ruler to be L B. These two results will be such that " A) L A > L B. " B) L A = L B. " C) L A < L B. " D) L A could be greater or smaller than L B depending on the direction of the motion. " Answer: C " 8. You are moving at a speed (2/3) c relative to Randy, and Randy shines a light toward you. At what speed do you see the light passing you by? " A) (1/3) c " B) (2/3) c " C) (4/3) c " D) c " E) It depends on whether you are moving towards or away from Randy. " Answer: D "
9. Astronaut Jill leaves Earth in a spaceship and is now traveling at a speed of 0.280 c relative to an observer on Earth. When Jill left Earth, the spaceship was equipped with all kinds of scientific instruments, including a meter stick. Now that Jill is underway, how long does she measure the meter stick to be? " A) 1.00 m " B) 0.960 m " C) 1.04 m " D) 0.280 m " E) 1.28 m " Answer: A Meter stick is in Jill’s frame – an Earth observer would see it contracted, but not Jill. 10. At what speed is the mass of an electron double its rest mass? " A) 0.500 c " B) 0.650 c " C) 0.707 c " D) 0.866 c " E) 0.960 c " Answer: D " 11. Which one of the following is true for the surface temperature T of a bluish-white star, as compared to a red star? " A) Blue star # s T is greater. " B) Blue star # s T is less. " C) Blue star # s T is the same. " Answer: A " I hope you remember (after all our discussions of spectra) that red = long wavelength, blue=short wavelength, and shorter wavelength =higher frequency! Temperature is proportional to f: "
12. A photon has energy of 4.20 eV. To what wavelength does this energy correspond? " A) 321 nm " B) 103 nm " C) 296 nm " D) 412 nm " E) 420 nm " Answer: C "
13. The work function of a certain metal is 1.90 eV. What is the longest wavelength of light that can cause photoelectron emission from this metal? " A) 231 nm " B) 14.0 nm " C) 62.4 nm " D) 344 nm " E) 653 nm " Answer: E " (see practice questions!) " 14. An electron is moving with the speed of 1780 m/s. What is its de Broglie wavelength? " A) 409 nm " B) 302 nm " C) 205 nm " D) 420 nm " E) 502 nm " Answer: A " (see practice questions!) "
15. A muon is an unstable particle that has an average lifetime of 1.52 � 10-6 s. This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the muon. An "average" muon is observed by a scientist on Earth to travel 342 m in its lifetime. What is the speed of the muon relative to Earth? " A) 0.821 c " B) 0.681 c " C) 0.601 c " D) 0.551 c " E) 0.335 c " Answer: C " The muon # s lifetime in the Earth frame is time-dilated by the Lorentz factor, so "
More details on the structure of atoms • � With the work of Schrödinger and Heisenberg, we can complete our picture of atomic structure – � Quantum mechanics allows exact computations for any atom, not just hydrogen or helium: chemistry is no longer empirical • � Each atom’s electron arrangement is described by a set of “quantum numbers” (integers or half-integers – sound familiar?) – � Principal quantum number (energy level) n=0,1,2,3… – � Orbital number (value of angular momentum L due to e’s orbital motion) l =0,1,2…n – � “magnetic” quantum number m l (component of L along some axis) • � …for example, a symmetry axis: the magnetic field direction, if B is present • � Exclusion principle -> cannot know more than 1 component of L precisely – � “spin” quantum number m s (“internal” angular momentum of electron) • � Only 2 values allowed: spin = +1/2 (“spin up”) or -1/2 (“spin down”) • � Relative to axis used for l - also in units of h-bar 11
Example: hydrogen for n=1 and n=2 • � Table in text shows all the allowed “quantum states” for the single electron in a hydrogen atom “Ground state” has n=1, l =0, (only allowed value) Spin either up or down: 2 possible states first “excited state” has n=2, l =0 spin either up or down: 2 possible states next excited state has n=2, l =1, m l = -1, 0, or +1 spin either up or down for each value of l 6 possible states 12
Better than the popcorn ball picture… • � Here are electron ‘orbitals’ for a hydrogen atom (maps of charge density, or probability of finding electron) • � Numbers give the electron’s quantum energy level (here, the 2 nd and 3 rd ) • � Letters give its quantized angular momentum (s=0, p=1, d=2 quanta of L) – � Letters are labels from 19 th c. studies of atomic spectra • � Quantum theory connects line spectra with levels – � Notice: • � s orbitals are spherically symmetrical • � p’s have 1 axis of symmetry • � d’s have 2 symmetry axes… etc 13 http://www.chemistry.mcmaster.ca/esam
Lasers: atomic physics and QM in action • � Laser processes – � Three possible atom-photon interactions (Einstein, 1916): 1. � Electron absorbs a photon, pops into a higher E level 2. � Electron in higher E level randomly falls to lower state, emitting a photon 3. � Electron in higher E level falls to ground state and emits a photon when stimulated by a photon of the same wavelength For spontaneous emission, the emitted photon is in phase: the photons are coherent (in phase) Absorption Spontaneous emission Stimulated emission – � To get useful light output, we must “pump” atoms into a metastable* higher state: population inversion normal state occupancy population inversion *not stable like the ground E 2 E 2 state, but comparatively E 1 E 1 long average lifetime E 0 E 0 % of atoms % of atoms – � Optical pumping: use flash lamp to raise atoms to a state E 2 above E 1 = metastable state
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