How Is Kinetic Energy Transformed in Nuclear Fusion Reactions?

In summary, fusion reactions involve the joining of two atoms' nuclei to form a new element, with a conversion of some rest energy to kinetic energy. This process can occur in the Sun, converting hydrogen to helium without involving electrons. An experimental apparatus can also cause fusion reactions by bringing two nuclei close enough to react and produce a helium-3 nucleus and a gamma ray. The kinetic energy of the reaction products can be calculated using the equation Kf + Uf = Ki+Ui, where Uf is the final potential energy and Ui is the initial potential energy. If a mole of hydrogen and a mole of deuterium undergo this fusion reaction, a significant amount of kinetic energy would be generated.
  • #1
astros10
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Homework Statement


In a fusion reaction, the nuclei of two atoms join to form a single atom of a different element. In such a reaction, a fraction of the rest energy of the original atoms is converted to kinetic energy of the reaction products. A fusion reaction that occurs in the Sun converts hydrogen to helium. Since electrons are not involved in the reaction, we focus on the nuclei.
Hydrogen and deuterium (heavy hydrogen) can react to form helium plus a high-energy photon called a gamma ray:

Particle # of protons # of neutrons Charge Rest Mass (atomic mass units)
1H (proton) 1 0 +e 1.0073
2H (deuterium) 1 1 +e 2.0136
3He (helium) 2 1 +2e 3.0155
gamma ray 0 0 0 0

A proton (1H nucleus) and a deuteron (2H nucleus) start out far apart. An experimental apparatus shoots them toward each other (with equal and opposite momenta). If they get close enough to make actual contact with each other, they can react to form a helium-3 nucleus and a gamma ray (a high energy photon, which has kinetic energy but zero rest energy). Consider the system containing all particles.

A)The deuterium nucleus starts out with a kinetic energy of 6.2e-14 joules, and the proton starts out with a kinetic energy of 1.23e-13 joules. The radius of a proton is 0.9e-15 m; assume that if the particles touch, the distance between their centers will be twice that. What will be the total kinetic energy of both particles an instant before they touch?



B) Now that the proton and the deuterium nucleus are touching, the reaction can occur. 1.What is the kinetic energy of the reaction products (helium nucleus plus photon)?

2.What was the gain of kinetic energy in this reaction? (The products have more kinetic energy than the original particles did when they were far apart. How much more?)

3. If a mole of hydrogen and a mole of deuterium underwent this fusion reaction, how much kinetic energy would be generated?


Homework Equations


c (speed of light)= 2.9979e8 m/s
e (charge of a proton) =1.6022e-19 coulomb
atomic mass unit =1.6605e-27 kg
coulomb's constant=8.9875e9 N·m2 /C2
Kf + Uf = Ki+Ui
U=-(GMm)/R



The Attempt at a Solution


The only one I have attempted thus far is A because I believe I need that answer to solve the three questions in part B. What I did for the first part was take:

Kf + Uf = Ki+Ui
Ui=0, Ki=6.2e-14j+1.23e-13j
Could the answer to the first part be 0 for the final kinetic energy, since all the energy has been transferred to potential energy?
 
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  • #2
astros10 said:

Homework Equations


Kf + Uf = Ki+Ui
U=-(GMm)/R
The last formula is for the gravitational potential energy of two point masses (or spherical masses). Gravity is not relevant here.

astros10 said:

The Attempt at a Solution


The only one I have attempted thus far is A because I believe I need that answer to solve the three questions in part B. What I did for the first part was take:

Kf + Uf = Ki+Ui
Ui=0, Ki=6.2e-14j+1.23e-13j
Could the answer to the first part be 0 for the final kinetic energy, since all the energy has been transferred to potential energy?
No. You need to calculate Uf and then substitute into your equation
Kf + Uf = Ki+Ui
 

1. What is a fusion reaction?

A fusion reaction is a process in which two or more atomic nuclei combine to form a heavier nucleus, releasing a large amount of energy in the process. This is the same process that powers the sun and other stars.

2. What is the goal of achieving a fusion reaction?

The goal of achieving a fusion reaction is to harness the energy released to generate electricity in a clean and sustainable manner, without producing harmful greenhouse gas emissions or radioactive waste.

3. What are the challenges in achieving a fusion reaction?

One of the main challenges in achieving a fusion reaction is creating and maintaining the extreme conditions necessary for fusion to occur, such as extremely high temperatures and pressures. Another challenge is containing the hot plasma (a state of matter in which atoms are stripped of their electrons) in a stable manner using magnetic fields.

4. How close are we to achieving a fusion reaction?

Scientists and engineers have made significant progress in fusion research and have successfully produced fusion reactions in various experiments. However, there are still many challenges to overcome before fusion can be harnessed as a reliable source of energy on a large scale.

5. What are the potential benefits of a successful fusion reaction?

If a successful fusion reaction can be achieved, it has the potential to provide a nearly limitless source of clean, safe, and sustainable energy. It could also reduce our dependence on fossil fuels and help mitigate the effects of climate change. Additionally, fusion reactors do not produce long-lived radioactive waste, making them a much safer alternative to nuclear fission reactors.

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