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
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
- (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_forward(a) Calculate the radius of 58Ni, one of the most tightly bound stable nuclei. (b) What is the ratio of the radius of 58Ni to that at 258Ha, one of the largest nuclei ever made? Note that the radius of the largest nucleus is still much smaller than ?le size of an atom.arrow_forward(a) Calculate the energy released in the a decay of 238U . (b) What fraction of the mass of a single 238U is destroyed in the decay? The mass of 234Th is 234.043593 u. (c) Although the fractional mass loss is large for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?arrow_forward
- (a) Calculate the energy released in the neutron- Induced fission reaction n+235U92Kr+142Ba+2n , given m(92Kr) = 91.926269 u and m(142Ba)= 141.916361 u. (b) Confirm that the total number of nucleons and total charge are conserved in this reaction.arrow_forward(a) Calculate the energy released in the a decay of 238U. (b) What fraction of the mass at a single 238U is destroyed in the decay? The mass of 234Th is 234.043593 u. (c) Although the fractional mass loss is laws for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?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