A uranium nucleus (²3QU) moves along the positive x-axis with speed vy = 5.0 x 105 m/s when it decays into an a-particle (3He, helium nucleus) and a thorium nucleus (238Th). If ¿He moves off at an angle of 20.2° above the x-axis with a speed vHe = 1.4 × 107 m/s, you will determine what is the recoil velocity, Vrh, of 233Th and the angle below the x-axis. Assume the uranium-thorium-alpha system is isolated with not external forces acting on it and the masses of are A x 1.673 x 10-27 kg. Please note that in the abbreviation, 4X, X is the atomic abbreviation, Z the number of protons in the nucleus and A the total number of nucleons (protons plus neutrons). This is a two-dimensional problem. (a) Write an expression for the conservation of momentum in the x direction in terms of the masses (ma mrn) the velocities (va, Vrn) and angles (6a,0Tn) measured from the x-axis. (b) Repeat (a) for the y-direction assuming up is positive. (c) Write an expression for tan 0Th in terms of the masses, velocities and Oa. (d) Write an expression for vrh in terms of ma, M™h, Va, Oa and OTh. (e) Evaluate Orn and vrn-
A uranium nucleus (²3QU) moves along the positive x-axis with speed vy = 5.0 x 105 m/s when it decays into an a-particle (3He, helium nucleus) and a thorium nucleus (238Th). If ¿He moves off at an angle of 20.2° above the x-axis with a speed vHe = 1.4 × 107 m/s, you will determine what is the recoil velocity, Vrh, of 233Th and the angle below the x-axis. Assume the uranium-thorium-alpha system is isolated with not external forces acting on it and the masses of are A x 1.673 x 10-27 kg. Please note that in the abbreviation, 4X, X is the atomic abbreviation, Z the number of protons in the nucleus and A the total number of nucleons (protons plus neutrons). This is a two-dimensional problem. (a) Write an expression for the conservation of momentum in the x direction in terms of the masses (ma mrn) the velocities (va, Vrn) and angles (6a,0Tn) measured from the x-axis. (b) Repeat (a) for the y-direction assuming up is positive. (c) Write an expression for tan 0Th in terms of the masses, velocities and Oa. (d) Write an expression for vrh in terms of ma, M™h, Va, Oa and OTh. (e) Evaluate Orn and vrn-
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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Transcribed Image Text:A uranium nucleus (²3QU) moves along the positive x-axis with speed vy = 5.0 x 105 m/s when it decays
into an a-particle (3He, helium nucleus) and a thorium nucleus (238Th). If ¿He moves off at an angle of
20.2° above the x-axis with a speed vHe = 1.4 × 107 m/s, you will determine what is the recoil velocity,
Vrh, of 233Th and the angle below the x-axis. Assume the uranium-thorium-alpha system is isolated with
not external forces acting on it and the masses of are A x 1.673 x 10-27 kg. Please note that in the
abbreviation, 4X, X is the atomic abbreviation, Z the number of protons in the nucleus and A the total
number of nucleons (protons plus neutrons). This is a two-dimensional problem.
(a) Write an expression for the conservation of momentum in the x direction in terms of the masses
(ma mrn) the velocities (va, Vrn) and angles (6a,0Tn) measured from the x-axis.
(b) Repeat (a) for the y-direction assuming up is positive.
(c) Write an expression for tan 0Th in terms of the masses, velocities and Oa.
(d) Write an expression for vrh in terms of ma, M™h, Va, Oa and OTh.
(e) Evaluate Orn and vrn-
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