# Energy in a fusion reaktion (Have I done it right?)

• Ante
In summary, energy in a fusion reaction is the release of energy when two atomic nuclei combine. This process is powered by the conversion of mass into energy and has the potential to provide limitless clean energy. However, there are challenges in initiating and harnessing fusion reactions, and it may take several decades before fusion energy can be used commercially.
Ante

## Homework Statement

The deuterium nucleus starts out with a kinetic energy of 1.09e-13 joules, and the proton starts out with a kinetic energy of 2.19e-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.

A: What will be the total kinetic energy of both particles an instant before they touch?

B: What is the kinetic energy of the reaction products (helium nucleus plus photon)?

C: 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?)

D: Kinetic energy can be used to drive motors and do other useful things. If a mole of hydrogen and a mole of deuterium underwent this fusion reaction, how much kinetic energy would be generated?

## Homework Equations

E_U= (1/(4(Pi)(Epsilon_0)))*(q_1*q_2)/r

E_F=E_i

## The Attempt at a Solution

A: Used the law of energy conservation
E=(1/(4(Pi)(Epsilon_0)))*(q_1*q_2)/r -(k_i)

B: Potential energy becomes kinetic energy: E=(1/(4(Pi)(Epsilon_0)))*(q_1*q_2)/r = K

C: (1/(4(Pi)(Epsilon_0)))*(q_1*q_2)/r - (k_i)

D:

One mole deuterium = 6.02*10^2p
One mol protons = 6.02*10^2p
One mole gives: 7.326*10^10 J

or 73.26 GJ

A: The total kinetic energy of both particles an instant before they touch would be the sum of their individual kinetic energies, so it would be 1.09e-13 J + 2.19e-13 J = 3.28e-13 J.

B: The kinetic energy of the reaction products can be found by subtracting the total kinetic energy of the initial particles from the total kinetic energy before the reaction, so it would be 3.28e-13 J - (1.09e-13 J + 2.19e-13 J) = 0 J.

C: The gain of kinetic energy in this reaction would be the difference between the kinetic energy of the reaction products and the initial particles, so it would be 0 J - (1.09e-13 J + 2.19e-13 J) = -3.28e-13 J. This means that the products have 3.28e-13 J less kinetic energy than the initial particles.

D: To calculate the kinetic energy generated by one mole of hydrogen and deuterium undergoing this fusion reaction, we can use the formula E = mc^2, where m is the mass of the reactants and c is the speed of light. The mass of one mole of hydrogen and deuterium is 2 grams, or 0.002 kg. The speed of light is approximately 3 x 10^8 m/s. Plugging these values into the equation, we get E = (0.002 kg)(3 x 10^8 m/s)^2 = 1.8 x 10^14 J. This is equivalent to 180 TJ (terajoules) or 180,000 GJ (gigajoules).

## What is energy in a fusion reaction?

Energy in a fusion reaction refers to the release of energy that occurs when two atomic nuclei combine to form a heavier nucleus. This process, known as fusion, is the same process that powers the sun and other stars.

## How is energy released in a fusion reaction?

Energy is released in a fusion reaction due to the conversion of mass into energy, as described by Einstein's famous equation E=mc². When two atomic nuclei fuse, a small amount of mass is lost, which is then converted into a large amount of energy.

## What are the potential benefits of fusion energy?

Fusion energy has the potential to provide a virtually limitless source of clean and sustainable energy. It produces no greenhouse gases or long-lived radioactive waste, making it a promising alternative to fossil fuels for meeting our energy needs.

## What are the challenges facing fusion energy research?

Fusion energy research faces several challenges, including the high temperatures and pressures required to initiate and sustain fusion reactions, as well as the difficulty of confining and controlling the extremely hot plasma needed for fusion. Additionally, the technology for harnessing fusion energy on a large scale is still in development.

## When can we expect to see fusion energy being used commercially?

While significant progress has been made in fusion energy research, it is difficult to predict when fusion energy will become a viable commercial energy source. Many experts estimate that it will still take several decades before fusion power plants are operational and able to contribute to our energy needs.

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