Download PHY112-‐Spring 14, Worksheet 4

PHY112-­‐Spring 14, Worksheet 4 Due Apr 29 Conceptual Problems 1. A light source with intensity 𝐼! (measured in !
!!
=
!
! !!
) and frequency 𝑓 is shone on an electrode made of a metal whose cutoff frequency 𝑓!"#!!"" is less than 𝑓 , thereby generating a photoelectric current. If the frequency of the light source is doubled to 2𝑓, while the intensity of the light source remains unchanged at 𝐼! , the number of photons from the light source which hit the electrode per unit time will ___________, and the percentage of those incoming photons which ionize an electron from the electrode will ___________. a. increase; increase b. increase; decrease c. not change; increase d. not change; decrease e. decrease; increase f. decrease; decrease 2. According to the ordering scheme we have used, how many electrons in a neutral Xenon atom have angular quantum number ℓ𝓁 = 2 and spin-­‐component quantum number 𝑚! = +1/2? a. 0 b. 4 c. 5 d. 10 3. In one nuclear reaction, a single proton collides with a nucleus of Mercury-­‐200. One product of the reaction is an 𝛼 -­‐particle (a Helium-­‐4 nucleus). What nucleus is the other product of the reaction? a. Thallium-­‐201 b. Thallium-­‐197 c. Platinum-­‐196 d. Gold-­‐197 4. On a normal day in Rome with temperature 80°F (300 K), the white sidewalks on the Berry campus emit ______ within the visual spectrum, ______ within the infrared spectrum. a. a wide range of frequencies; but no frequencies b. a wide range of frequencies; as well as frequencies characteristic of a blackbody at 300 Kelvin c. no frequencies; but frequencies characteristic of a blackbody at 300 Kelvin d. one frequency; but no frequencies 1 5. In contrast to Thomson’s model (plum-­‐pudding model) of the atom, Rutherford’s model: a. had the positive charge spread uniformly through the atom. b. had the positive charge concentrated in a small region. c. was first to explain atoms emitting discrete frequencies. d. eliminated radiation from accelerating charges. 6. In the Bohr model of the atom, the orbits where electrons move fastest: a. have the lowest energy. b. have the highest energy. c. have the biggest radius. d. have the greatest angular momentum. Calculational Problems 7. In a double-­‐slit interference experiment, a screen is placed 2.00 m behind the double slits. Light with a wavelength of 𝜆 = 480.0 nm is shone through the slits. The distance from the center of the diffraction pattern to the first dark fringe is measured to be 2.80 cm. a. How far apart are the two slits? b. What is the distance between the 𝑚 = 1 and 𝑚 = 2 bright fringes of the double-­‐slit pattern? c. If one of the two slits is then covered, the width of the central maximum in the resulting single-­‐slit diffraction pattern appearing on the screen is measured to be 1.10 m. What is the width of the (uncovered) slit? 8. You are working on a biochemistry project which requires a beam of electrons with speeds in a narrow range around the value 𝑣 = 6.50×10! m/s. To make this beam, you decide to set up a heated cathode which emits electrons, with kinetic energies ranging from 0.00 to 2.00 eV, toward a material which functions as a diffraction grating for electrons. Then you plan to select the electrons which emerge from the diffraction grating at the particular angle for which the !
electrons have the desired speed. Recall that kinetic energy 𝐾𝐸 = 𝑚𝑣 ! . !
a. What is the kinetic energy (in eV) of an electron with speed 𝑣 = 6.50×10! m/s? Does that kinetic energy in fact fall in the range of kinetic energies produced by your heated cathode? b. What are the momentum and the de Broglie wavelength of an electron with speed 𝑣 = 6.50×10! m/s? c. the effective slit separation of the diffraction grating is 𝑑 = 8.20×10!! m, at what diffraction angle will the first bright fringe for electrons with speed 𝑣 = 6.50×10! m/s occur? 2 9. In a nuclear magnetic resonance (NMR) experiment, a magnetic field with magnitude 4.00 T is applied to a sample containing a significant percentage of Carbon-­‐13 atoms. a. What is the energy of a !"C nucleus whose magnetic moment is aligned against the applied magnetic field? b. What are the frequency and the wavelength of the electromagnetic radiation would be emitted when the !"C nuclei drop from their higher energy state (aligned against the magnetic field) to their lower energy state (aligned with the magnetic field)? 10. In one type of treatment for thyroid cancer, a patient ingests a solution containing the radioactive isotope !"!
!"I (Iodine-­‐131), which is absorbed by the thyroid. The radioactive emissions from the 𝛽 ! decay of Iodine-­‐131 then preferentially kill cancer cells within the thyroid. A patient is administered a solution containing 0.300 𝑔 of iodine. The iodine is predominantly the common, non-­‐radioactive isotope Iodine-­‐127, but 1 part per billion (i.e., one atom out of each billion iodine atoms) is Iodine-­‐131. The Iodine-­‐131 atoms undergo 𝛽 ! decay with a half-­‐life of 8.04 days. The atomic weights of Iodine-­‐127 and Iodine-­‐131 are 126.904 u and 130.906 u, respectively. a. How many total iodine atoms are in the 0.300 g of iodine administered to the patient? (Hint: you may make the approximation that all of the iodine atoms have the atomic mass of Iodine-­‐127 in this calculation.) How many Iodine-­‐131 atoms are administered to the patient? b. Write down the products of the 𝛽 ! decay of Iodine-­‐131, including the daughter nucleus and any other particles emitted. Write any nuclei in the standard nuclear notation !!S. c. How long would it take for 99.0% of the Iodine-­‐131 atoms to decay? 3