Nuclear Fusion Reaction In a human-scale model of a nuclear fusion reaction, two "deuterons" smash together head-on. Each has a mass of 2.0147kg and is moving at speed va- The result is a "Helium-3 nucleus" (mass 3.0160kg) and a separate "neutron" (mass 1.0090kg). Amazingly, this reaction produces a positive Wne of 3.96 × 1014 J -- by converting mass into kinetic energy as predicted by Einstein's E = mc². The "neutron" moves with a speed of v₂ after the reaction. E + + D D ³He N. Proton Neutron http://fusion.srubar.net 4 Vd 1.57×107 m (no answer) Correct Answer: 3.64 Un x10m S

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)...
icon
Related questions
Question
Nuclear Fusion Reaction
In a human-scale model of a nuclear fusion reaction, two
"deuterons" smash together head-on. Each has a mass of
2.0147kg and is moving at speed vd.
The result is a "Helium-3 nucleus" (mass 3.0160kg) and a separate
"neutron" (mass 1.0090kg). Amazingly, this reaction produces a
positive Wnc of 3.96 × 10 14 J -- by converting mass into kinetic
energy as predicted by Einstein's E mc²
=
The "neutron" moves with a speed of un after the reaction.
E
4
☑
Vd
1.57×107 m
(no answer)
Correct Answer: 3.64
S
Un
×107 m
S
+
+
D D
3Не
N.
Proton
Neutron
http://fusion.srubar.net
Transcribed Image Text:Nuclear Fusion Reaction In a human-scale model of a nuclear fusion reaction, two "deuterons" smash together head-on. Each has a mass of 2.0147kg and is moving at speed vd. The result is a "Helium-3 nucleus" (mass 3.0160kg) and a separate "neutron" (mass 1.0090kg). Amazingly, this reaction produces a positive Wnc of 3.96 × 10 14 J -- by converting mass into kinetic energy as predicted by Einstein's E mc² = The "neutron" moves with a speed of un after the reaction. E 4 ☑ Vd 1.57×107 m (no answer) Correct Answer: 3.64 S Un ×107 m S + + D D 3Не N. Proton Neutron http://fusion.srubar.net
Solution:
Conservation of momentum:
mava + ma(-va) = Mn Vn + MH (-VH)
Solve for VH:
VH
=
Mn
ΜΗ
Un (Eqn. 1)
Conservation of energy (with positive Wnc):
2 (mav²) + Wne = ½ m² v²/₁₂ + ½ mн V²/
пс
Plug in for VH from (Eqn. 1):
2 (mav²) + Wnc = m₁v² + ½ m
Clean up:
пс
mav²/2 + Wnc = 1 / (mn +
m²
ΜΗ
ບ
Plug in masses of "particles" and Wnc:
Mn Un
ΜΗ
2)²
(2.0147kg) + (3.96 × 10 14 J) = (.6733kg)v
Transcribed Image Text:Solution: Conservation of momentum: mava + ma(-va) = Mn Vn + MH (-VH) Solve for VH: VH = Mn ΜΗ Un (Eqn. 1) Conservation of energy (with positive Wnc): 2 (mav²) + Wne = ½ m² v²/₁₂ + ½ mн V²/ пс Plug in for VH from (Eqn. 1): 2 (mav²) + Wnc = m₁v² + ½ m Clean up: пс mav²/2 + Wnc = 1 / (mn + m² ΜΗ ບ Plug in masses of "particles" and Wnc: Mn Un ΜΗ 2)² (2.0147kg) + (3.96 × 10 14 J) = (.6733kg)v
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Knowledge Booster
Relativistic Energy and momentum
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
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…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON