1. Image that two particles, a proton and an electron, are confined to move on circular rings of fixed radius, r. For each particle, the kinetic energy can be written as т 1 T = 5(v,² + v,²) =;lo? 2 where the angular velocity, w = de and the moment of inertia, I = mr², arise from dt' converting this expression from Cartesian to plane polar coordinates. (a) Let the fixed radius for each particle be r = ao. Suppose that both the proton and the electron can be treated classically and that they happen to have the same angular momentum, L = lw. What would be the ratio of their angular velocities, "electron? @proton Note- the physical constants you need are listed at the end of this problem set. (b) Now, suppose both the proton and the electron have the same angular velocity, a, but are on rings of different sizes. If the proton's ring has radius r = 2a, = 105.83 pm (twice the Bohr radius), and the two particles have identical angular momentum, L, what is the radius of the electron's ring (in pm)? %3D (c) For the case examined in part (a) (same ring with same angular momentum), what is the ratio of the electron's kinetic energy to that of the proton? (Report to four significant figures.)
1. Image that two particles, a proton and an electron, are confined to move on circular rings of fixed radius, r. For each particle, the kinetic energy can be written as т 1 T = 5(v,² + v,²) =;lo? 2 where the angular velocity, w = de and the moment of inertia, I = mr², arise from dt' converting this expression from Cartesian to plane polar coordinates. (a) Let the fixed radius for each particle be r = ao. Suppose that both the proton and the electron can be treated classically and that they happen to have the same angular momentum, L = lw. What would be the ratio of their angular velocities, "electron? @proton Note- the physical constants you need are listed at the end of this problem set. (b) Now, suppose both the proton and the electron have the same angular velocity, a, but are on rings of different sizes. If the proton's ring has radius r = 2a, = 105.83 pm (twice the Bohr radius), and the two particles have identical angular momentum, L, what is the radius of the electron's ring (in pm)? %3D (c) For the case examined in part (a) (same ring with same angular momentum), what is the ratio of the electron's kinetic energy to that of the proton? (Report to four significant figures.)
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:1. Image that two particles, a proton and an electron, are confined to move on circular rings of
fixed radius, r. For each particle, the kinetic energy can be written as
т
1
T = 5(v,² + v,²) =;lo?
2
where the angular velocity, w =
de
and the moment of inertia, I = mr², arise from
dt'
converting this expression from Cartesian to plane polar coordinates.
(a) Let the fixed radius for each particle be r = ao. Suppose that both the proton and the
electron can be treated classically and that they happen to have the same angular
momentum, L = lw. What would be the ratio of their angular velocities, "electron?
@proton
Note- the physical constants you need are listed at the end of this problem set.
(b) Now, suppose both the proton and the electron have the same angular velocity, w, but
are on rings of different sizes. If the proton's ring has radius r = 2ao
(twice the Bohr radius), and the two particles have identical angular momentum, L, what
is the radius of the electron's ring (in pm)?
105.83 pm
%3D
(c) For the case examined in part (a) (same ring with same angular momentum), what is the
ratio of the electron's kinetic energy to that of the proton? (Report to four significant
figures.)
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