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PHYS 203 General Physics Final Exam Review Sheet The final exam is Monday, June 7, at 1:00 pm. The exam will be comprehensive. It will be closed book. All necessary equations will be provided, but you may bring a 3 × 5 card with equations written on it if you wish. You are also responsible for George Gamow’s book, Chapters 1 through 6. Look over the Mid-term Review Sheets for other study problems. Following are some problems from previous final exams. Also, there is a sample final exam available on the class web site. Finally, Review your labs. 1. (This was on the Midterm 2 review sheet also.) Things to memorize: (1) the wavelength ranges for IR, visible, and UV light, in nm; (2) the approximate size of an atom; (3) the approximate size of a nucleus; (4) the approximate size of a bacterium; (5) the approximate size of a human hair; (6) the velocity of light; and (7) the accepted age of the universe. 2. Suppose you shine light through a diffraction grating in which the grooves (or scratches) are 4.00 µm apart. You observe a 3rd-order maximum at an angle of 25◦ from the central maximum. (A) What is the wavelength of the light? (B) Suppose you repeat the experiment under water. At what angle would you see the 3rd-order maximum now? 3. Suppose a laser beam is directed onto the flat surface of a piece of transparent plastic, and an angle 70◦ from the normal. The angle of refraction (when the beam enters the material) is measured to be 36.0◦ . What is the index of refraction of the plastic? 4. Planck presented his Blackbody Formula, which introduced the idea of the quantum of energy, in 1900. About how long was it before quantum theory matured into a more or less complete theory? Why did it take this long? (Gamow has something to say about this.) 5. What is the Heisenberg Uncertainty Principle? What is there about it that Einstein did not like? 6. Know the contributions of each of the following to our understanding of the structure of the atom, or to our understanding of matter in general: Planck, de Broglie, Rutherford, Bohr, Einstein, and Dirac. 7. Early models of the atom assumed a large “soft” ball of positive charge with electrons embedded in it. What evidence do we have that this is wrong? 8. The mass energy of an electron is 0.511 MeV. What is the speed of an electron whose total energy is three times that, or 1.53 MeV? 9. Suppose that Planck’s constant h were to change from 6.6×10−34 J-s to 0.066 J-s. What kind of effects might you notice from this change? 10. The microwaves we used in the lab had wavelengths of about 3.2 cm. What is the energy of a photon with this wavelength? 11. A doubly-ionized Lithium atom has only a single electron, so the Bohr model can describe it. The red Balmer line from hydrogen is due to a n = 3 −→ n = 2 transition. What transition in doubly-ionized lithium will result in the same wavelength of emitted light? 12. The tracks of a CD (compact disk) are 1.60 µm apart. When laser light of a certain wavelength is shined onto a CD in a direction normal to the surface, a second-order interference maximum is observed at 34◦ from the normal. Find the wavelength of the laser light. 13. Police radar guns often use microwaves of frequency 24.2 GHz. What is the wavelength of these microwaves? What is the energy, in eV, of a microwave photon at this frequency? 14. Which of the physicists described in Gamow’s book was a duke? Who was Nicholas Baker? Who invented a wave equation which predicted 3-dimensional “standing waves” of electrons in atoms? Who invented the Uncertainty Principle? Which two physicists had a long-running debate over the “probabilistic” interpretation of quantum mechanics? Who predicted the existence of anti-matter? 15. Write down the nuclear reaction equation for 228 90 Th undergoing α-decay. − 22 16. Write down the equation for 24 11 Na undergoing β -decay (beta decay.) How about 11 Na undergoing β + -decay (positron emission)? 17. Suppose a hydrogen atom is excited by an electrical discharge and ends up in a state n = 7. It decays to n = 6 with emission of a photon. (A) What is the energy of this photon, in eV? (B) What is the wavelength of the photon? In what region of the spectrum is this? 18. A certain computer monitor (the old kind) accelerates electrons through a voltage of 3000 V: there is a 3000-V potential between the electron source and the screen. (A) Find the de Broglie wavelength of the electrons just before they hit the screen. (Note: you should first decide whether or not to use relativity, or just use the classical expression for kinetic energy.) (B) Find the minimum wavelength of x-rays that are emitted from the screen as a result of the electrons colliding with it. 19. Suppose an electron is send toward a small slit in a piece of metal, in vacuum. The slit is 2.0 µm wide. If the electron is headed in the “y” direction, we could call the plane of the slit the “x” direction. By localizing the electron in the x-direction, we introduced uncertainty in its momentum in that direction. We know the electron’s position, with an uncertainty ∆x ≈ ±1µm. 1 µm Use the Uncertainty Principle to estimate the un= half width certainty in its momentum along the x-direction. Then find the uncertainty in its velocity in the x-direction. (This is why the electrons diffract (spread out) and form a fuzzy diffraction pattern on a detector.) 20. 45 20 Ca is an isotope sometimes used in biochemistry. It decays by β − -decay, and its half-life is 164 days. (A) Find the decay constant λ of calcium-45. (B) If my sample of calcium-45 has an activity of 1000 Bq when it is produced, what will its activity be 1 year later? (C) Write down the nuclear reaction for the β-decay of 45 20 Ca. Answers to selected questions. #2 λ = 563 nm; θ = 18.5◦ . #3 n = 1.60 #8 √ 1 2 2 = 3, so v = 0.942c 1−v /c #10 3.4×10−5 eV #12 λ = 447 nm #17. E = 0.1002 eV; λ =12.37 µm: infrared. #18. (A) λ = 0.022 nm, (B) λmin =0.41 nm #19. ∆x ∆p ∼ h 4π so hc = 98.7 eV-nm 4π 98.7 eV-nm ≈ 0.1 eV ∆(pc) ∼ 1000 nm ∆x ∆(pc) ∼ Then ∆p works out to about 5×10−29 kg m/s. This small number shouldn’t surprise use since it is in SI units. The uncertainty in velocity is then (∆p)/m: ∆v = ∆p ∆(pc) 0.1 eV = c= (3×108 m/s) = 60 m/s 2 m mc 5×105 eV