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A 232Th (thorium) nucleus at rest decays to a 228Ra

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 102P Chapter 8

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 102P

A 232Th (thorium) nucleus at rest decays to a 228Ra (radium) nucleus with the emission of an alpha particle. The total kinetic energy of the decay fragments is 6.54 × 10?13 J. An alpha particle has 1.76% of the mass of a 228Ra nucleus. Calculate the kinetic energy of (a) the recoiling 228Ra nucleus and (b) the alpha particle.

Step-by-Step Solution:

Solution 102P Step 1: Initially the 232Th nucleus was at rest and decays into a 228Ra nucleus and an alpha particle. By the conservation of momentum, m V = m V --------------------(1) Ra Ra But it is given that, m 0.0176 m Ra -----------------(2) By putting this value in equation (1), m Ra Ra = 0.0176 m Ra V V = 0.0176 V ----------------------(3) Ra Step 2: The total kinetic energy would be, 1 2 1 2 1 2 2 K.E tot m2 RaV Ra + 2 V = [2 VRa Ra + 0.0176 m Ra V ] 1 2 V Ra = m2 Ra [V Ra + 0.0176 × 0.0176] 1 2 VRa2 1 2 1.0176 1 2 = m2 Ra [V Ra + 0.0176] = 2 Ra V Ra × 0.0176= 2 Ra V Ra × 57.81.

Step 3 of 3

Chapter 8, Problem 102P is Solved
Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

The full step-by-step solution to problem: 102P from chapter: 8 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. The answer to “A 232Th (thorium) nucleus at rest decays to a 228Ra (radium) nucleus with the emission of an alpha particle. The total kinetic energy of the decay fragments is 6.54 × 10?13 J. An alpha particle has 1.76% of the mass of a 228Ra nucleus. Calculate the kinetic energy of (a) the recoiling 228Ra nucleus and (b) the alpha particle.” is broken down into a number of easy to follow steps, and 59 words. This full solution covers the following key subjects: nucleus, alpha, particle, Energy, kinetic. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. Since the solution to 102P from 8 chapter was answered, more than 256 students have viewed the full step-by-step answer. University Physics was written by and is associated to the ISBN: 9780321675460. This textbook survival guide was created for the textbook: University Physics, edition: 13.

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