(a) Explanation Given Info: The radius of the proton ( r p ) is 1.2 × 10 − 15 m , and the mass of the proton ( m p ) is 1.67 × 10 − 27 kg . The nuclear fusion process occurs only when the proton’s surfaces are essentially in contact. Refer the figure 1, if the protons are in contact, then the distance between the protons closest approach is 2 r p , here r p is the radius of the proton. The charge of the proton is e . In nuclear fusion, during collision process the initial kinetic energy of the two particles is converted as the electric potential energy at the distance of the closest approach. Hence, for the repulsion process the initial kinetic energy is equal to the final potential energy of the protons. Formula to calculate the final electric potential energy of the protons is, U f = k q 1 q 2 r k is the proportionality constant, q 1 is the charge of the proton 1, q 2 is the charge of the proton 2, r is the distance of closest approach of the protons. Formula to calculate the initial kinetic energy of the two protons is, K i = 2 ( 1 2 m p v 2 ) m p is the mass of the proton, v is the minimum speed at the distance of closest approach of the protons. Formula to calculate the speed of proton using conservation of energy law is, K i = U f U f is the electric potential energy of the protons, K i is the initial kinetic energy of the protons. Substitute 1 2 m p v 2 for K i , and k q 1 q 2 r for U f to find v . 2 ( 1 2 m p v 2 ) = k q 1 q 2 r v 2 = k q 1 q 2 m p r v = k q 1 q 2 m p r Substitute 8.99 × 10 9 N ⋅ m 2 / C 2 for k , e for q 1 , e for q 2 , 1.67 × 10 − 27 kg for m p , and 2 r p for r to find v . v = ( 8.99 × 10 9 N ⋅ m 2 / C 2 ) ( e ) ( e ) ( 1 (b) To determine The minimum speed required to allow the nuclear fusion to occur between the two helium nuclei. (c) To determine The absolute temperature required for the nuclear fusion process undergone by the two protons and two heliums. (d) To determine To compare: The absolute temperature required for the nuclear fusion process undergone by the two protons and two heliums with the temperature in the sun’s core of about 1.5 × 10 7 K .

University Physics With Modern Physics Technology Update, Books A La Carte Edition

13th Edition

ISBN: 9780321898104

Author: Hugh D. Young, Roger A. Freedman

Publisher: Addison-wesley Longman

See similar textbooks

Question

Chapter 23, Problem 85E

(a)

To determine

The minimum speed required to allow the nuclear fusion to occur between the two protons.

(b)

To determine

The minimum speed required to allow the nuclear fusion to occur between the two helium nuclei.

(c)

To determine

The absolute temperature required for the nuclear fusion process undergone by the two protons and two heliums.

(d)

To determine

To compare: The absolute temperature required for the nuclear fusion process undergone by the two protons and two heliums with the temperature in the sun’s core of about 1.5×107 K.

Expert Solution & Answer

Chapter 23 Solutions

University Physics With Modern Physics Technology Update, Books A La Carte Edition

Ch. 23 - Prob. 1DQ Ch. 23 - Prob. 2DQ Ch. 23 - Prob. 3DQ Ch. 23 - Prob. 4DQ Ch. 23 - Prob. 5DQ Ch. 23 - Prob. 6DQ Ch. 23 - Prob. 7DQ Ch. 23 - Prob. 8DQ Ch. 23 - Prob. 9DQ Ch. 23 - Prob. 10DQ

Ch. 23 - Prob. 11DQ Ch. 23 - Prob. 12DQ Ch. 23 - Prob. 13DQ Ch. 23 - Prob. 14DQ Ch. 23 - Prob. 15DQ Ch. 23 - Prob. 16DQ Ch. 23 - Prob. 17DQ Ch. 23 - Prob. 18DQ Ch. 23 - Prob. 19DQ Ch. 23 - Prob. 20DQ Ch. 23 - Prob. 21DQ Ch. 23 - Prob. 1E Ch. 23 - Prob. 2E Ch. 23 - Prob. 3E Ch. 23 - Prob. 4E Ch. 23 - Prob. 5E Ch. 23 - Prob. 6E Ch. 23 - Prob. 7E Ch. 23 - Prob. 8E Ch. 23 - Prob. 9E Ch. 23 - Prob. 10E Ch. 23 - Prob. 11E Ch. 23 - Prob. 12E Ch. 23 - Prob. 13E Ch. 23 - Prob. 14E Ch. 23 - Prob. 15E Ch. 23 - Prob. 16E Ch. 23 - Prob. 17E Ch. 23 - Prob. 18E Ch. 23 - Prob. 19E Ch. 23 - Prob. 20E Ch. 23 - Prob. 21E Ch. 23 - Prob. 22E Ch. 23 - Prob. 23E Ch. 23 - Prob. 24E Ch. 23 - Prob. 25E Ch. 23 - Prob. 26E Ch. 23 - Prob. 27E Ch. 23 - Prob. 28E Ch. 23 - Prob. 29E Ch. 23 - Prob. 30E Ch. 23 - Prob. 31E Ch. 23 - Prob. 32E Ch. 23 - Prob. 33E Ch. 23 - Prob. 34E Ch. 23 - Prob. 35E Ch. 23 - Prob. 36E Ch. 23 - Prob. 37E Ch. 23 - Prob. 38E Ch. 23 - Prob. 39E Ch. 23 - Prob. 40E Ch. 23 - Prob. 41E Ch. 23 - Prob. 42E Ch. 23 - Prob. 43E Ch. 23 - Prob. 44E Ch. 23 - Prob. 45E Ch. 23 - Prob. 46E Ch. 23 - Prob. 47E Ch. 23 - Prob. 48E Ch. 23 - Prob. 49E Ch. 23 - Prob. 50E Ch. 23 - Prob. 51E Ch. 23 - Prob. 52E Ch. 23 - Prob. 53E Ch. 23 - Prob. 54E Ch. 23 - Prob. 55E Ch. 23 - Prob. 56E Ch. 23 - Prob. 57E Ch. 23 - Prob. 58E Ch. 23 - Prob. 59E Ch. 23 - Prob. 60E Ch. 23 - Prob. 61E Ch. 23 - Prob. 62E Ch. 23 - Prob. 63E Ch. 23 - Prob. 64E Ch. 23 - Prob. 65E Ch. 23 - Prob. 66E Ch. 23 - Prob. 67E Ch. 23 - Prob. 68E Ch. 23 - Prob. 69E Ch. 23 - Prob. 70E Ch. 23 - Prob. 71E Ch. 23 - Prob. 72E Ch. 23 - Prob. 73E Ch. 23 - Prob. 74E Ch. 23 - Prob. 75E Ch. 23 - Prob. 76E Ch. 23 - Prob. 77E Ch. 23 - Prob. 78E Ch. 23 - Prob. 79E Ch. 23 - Prob. 80E Ch. 23 - Prob. 81E Ch. 23 - Prob. 82E Ch. 23 - Prob. 83E Ch. 23 - Prob. 84E Ch. 23 - Prob. 85E Ch. 23 - Prob. 86E Ch. 23 - Prob. 87E Ch. 23 - Prob. 88E Ch. 23 - Prob. 89E Ch. 23 - Prob. 90E Ch. 23 - Prob. 91E Ch. 23 - Prob. 92E

Knowledge Booster

Recommended textbooks for you

College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON