Concept explainers
(a)
Find the closest distance between the center of the nuclei.
(a)
Answer to Problem 26P
The closest distance between the center of the nuclei is
Explanation of Solution
The deuterium-tritium fusion reaction,
Here, the tritium nucleus is at rest. The mass number of deuterium is
Write the formula for radius of the nuclei
Where,
Conclusion:
The closest distance between the center of the two nuclei is
Substitute equation (I) in the above equation and solve
Substitute
Thus, the closest distance between the center of the nuclei is
(b)
Find the electric potential energy at the closest distance between the center of the nuclei.
(b)
Answer to Problem 26P
The electric potential energy at the closest distance between the center of the nuclei is
Explanation of Solution
The closest distance between the center of the nuclei is
Write the formula for potential energy
Where,
Conclusion:
Substitute
Thus, the electric potential energy at the closest distance between the center of the nuclei is
(c)
The speed of the deuterium and tritium nuclei as they touch.
(c)
Answer to Problem 26P
The speed of the deuterium and tritium nuclei as they touch is
Explanation of Solution
The mass of deuterium is approximately
According to the law of conservation of momentum,
Substitute
Thus, the speed of the deuterium and tritium nuclei as they touch is
(d)
Find the minimum initial deuteron energy required to achieve fusion.
(d)
Answer to Problem 26P
The minimum initial deuteron energy required to achieve fusion is
Explanation of Solution
According to the law of conservation of energy,
Here,
The deuteron has been moving from the beginning (infinity), therefore the initial potential energy of deuteron is zero,
Write the formula for kinetic energy
Where,
Conclusion:
Substituting equation (V) in (IV),
Substitute (III) in the above equation,
Substitute
Thus, the minimum initial deuteron energy required to achieve fusion is
(e)
Why the fusion reaction occurs at much lower deuteron energies then the energy calculated in part (d).
(e)
Answer to Problem 26P
The fusion reaction occurs at much lower deuteron energies then the energy calculated must be possibly by tunneling through the potential energy barrier.
Explanation of Solution
Classically, the particle with energy
Therefore, the fusion reaction occurs at much lower deuteron energies then the energy calculated must be possibly by tunneling through the potential energy barrier.
Want to see more full solutions like this?
Chapter 45 Solutions
PHYSICS:F/SCI...W/MOD..-UPD(LL)W/ACCES
- (a) Calculate the number of grams of deuterium in an 80.000L swimming pool, given deuterium is 0.0150% of natural hydrogen. (b) Find the energy released in joules if this deuterium is fused via the reaction 2H+2H3He+n. (c) Could the neutrons be used to create more energy? (d) Discuss the amount of this type of energy in a swimming pool as compared to that in, say, a gallon of gasoline, also taking into consideration that water is far more abundant.arrow_forwardIf two nuclei are to fuse in a nuclear reaction, they must be moving fast enough so that the repulsive Coulomb force between them does not prevent them for getting within R1014mof one another. At this distance or nearer, the attractive nuclear force can overcome the Coulomb force, and the nuclei are able to fuse. (a) Find a simple formula that can be used to estimate the minimum kinetic energy the nuclei must have if they are to fuse. To keep the calculation simple, assume the two nuclei are identical and moving toward one another with the same speed v. (b) Use this minimum kinetic energy to estimate the minimum temperature a gas of the nuclei must have before a significant number of them will undergo fusion. Calculate this minimum temperature first for hydrogen and then for helium. (Hint: For fusion to occur, the minimum kinetic energy when the nuclei are far apart must be equal to the Coulomb potential energy when they are a distance R apart.)arrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College