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An Isotope Separator. Hydrogen has three isotopes 'H (m1 = mp),

An Isotope Separator. Hydrogen has three isotopes 'H (m1 = mp),

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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An Isotope Separator. Hydrogen has three isotopes 'H (m1 = mp), <H (m2 2mp), and H (m33mp), where mp is the mass of a proton (1.67 × 10-27 kg). You and your team are tasked with constructing an isotope separator that will separate a gas of mixed hydrogen isotopes. The gas first passes through a device that atomizes it (i.e., makes sure the atoms are separate, and do not form H2 molecules), and then ionizes the atoms (strips off their only electron) so that they have a net charge of +e. Next, the atoms (now positive ions) are accelerated between the plates of a parallel-plate capacitor with a voltage of 2.9 kV across it, and emerge through a hole in one of the plates as a beam. (a) What are the speeds of the three isotopes when they emerge from the capacitor plates? (b) The accelerated ions enter a region of uniform magnetic field oriented perpendicular to the velocity vector of the ion beam. What should be the magnitude of the magnetic field if you want the largest diameter of the three ion paths to be 22.0 cm? (c) If you are collecting the atoms after completing a half-circle, one collector should be located 22.0 cm from the point where the beam enters the magnetic field. Where should the other two be located? (a) Isotope ¹H Number i Units Isotope 2H Number i Units Isotope ³H Number i Units (b) Number i Units (c) Isotope ¹H Number i Units Isotope 2H Number i Units
Transcribed Image Text:An Isotope Separator. Hydrogen has three isotopes 'H (m1 = mp), <H (m2 2mp), and H (m33mp), where mp is the mass of a proton (1.67 × 10-27 kg). You and your team are tasked with constructing an isotope separator that will separate a gas of mixed hydrogen isotopes. The gas first passes through a device that atomizes it (i.e., makes sure the atoms are separate, and do not form H2 molecules), and then ionizes the atoms (strips off their only electron) so that they have a net charge of +e. Next, the atoms (now positive ions) are accelerated between the plates of a parallel-plate capacitor with a voltage of 2.9 kV across it, and emerge through a hole in one of the plates as a beam. (a) What are the speeds of the three isotopes when they emerge from the capacitor plates? (b) The accelerated ions enter a region of uniform magnetic field oriented perpendicular to the velocity vector of the ion beam. What should be the magnitude of the magnetic field if you want the largest diameter of the three ion paths to be 22.0 cm? (c) If you are collecting the atoms after completing a half-circle, one collector should be located 22.0 cm from the point where the beam enters the magnetic field. Where should the other two be located? (a) Isotope ¹H Number i Units Isotope 2H Number i Units Isotope ³H Number i Units (b) Number i Units (c) Isotope ¹H Number i Units Isotope 2H Number i Units
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