What is the energy released in the fusion reaction:
2H+2H--> 4He + Q?
How do I calculate this?
H + H --> He + Q
where the H is H2, Deuterium, Hydrogen with a proton and a neutron
The helium-4 atoms are less massive than the two hydrogen atoms that started the process, so the difference in mass is converted to energy as described by Einstein's theory of relativity (E=mc²). The energy is emitted in various forms of light: ultraviolet light, X-rays, visible light, infrared, microwaves and radio waves.
So you need the mass of a Helium atom and the mass of 2 Deuterium atoms. the difference is m in E = m c^2
You need accurate values for the masses of 2H (a deuteron) and 4He (an alpha particle). Compute the mass loss in the reaction and multiply it by c^2. (Einstein's formula)
You could also use mass values of neutral deuterium and helium atoms, since the number of electrons is the same on both sides.
You can find the nuclear masses you need here:
http://fusedweb.pppl.gov/CPEP/Chart_Pages/3.HowFusionWorks.html
According to
http://en.wikipedia.org/wiki/Nuclear_fusion
that reaction does not occur in a single step.
To calculate the energy released in a fusion reaction, you can use Einstein's equation, E=mc^2. This equation relates energy (E) to mass (m) and the speed of light (c). In a fusion reaction, the total mass before the reaction equals the total mass after the reaction.
Let's break down the equation:
1. Find the total mass before the reaction:
- In this case, the total mass before the reaction is the sum of the masses of two hydrogen nuclei (2H). The mass of a hydrogen nucleus is approximately 1 atomic mass unit (amu). Therefore, the total mass before the reaction is 2 amu (1 amu + 1 amu).
2. Find the total mass after the reaction:
- In this case, the total mass after the reaction is the mass of four helium nuclei (4He). The mass of a helium nucleus is approximately 4 amu. Therefore, the total mass after the reaction is 4 amu (4 amu + 0 amu + 0 amu + 0 amu).
3. Calculate the mass difference:
- Subtract the total mass after the reaction from the total mass before the reaction to find the mass difference. In this case, the mass difference is 2 amu - 4 amu = -2 amu.
4. Convert the mass difference to energy:
- Use Einstein's equation, E=mc^2, to calculate the energy released. Since the mass difference is -2 amu, we need to use the positive value for the mass difference in the equation. The speed of light (c) is approximately 3 x 10^8 meters per second.
- E = (-2 amu) * (3 x 10^8 m/s)^2
Finally, calculate the value of E to get the energy released in the fusion reaction.
To calculate the energy released in the fusion reaction, let's break it down step by step.
1. First, we need to determine the mass of the reactants (2H and 2H) and the product (4He). The atomic mass of hydrogen (H) is approximately 1 atomic mass unit (u), and the atomic mass of helium (He) is approximately 4 u.
2. Next, we need to calculate the total mass of the reactants (2H + 2H) and the total mass of the product (4He).
Total mass of reactants = 2H + 2H = 2 × 1 u + 2 × 1 u = 4 u
Total mass of product = 4He = 4 × 4 u = 16 u
3. The law of conservation of mass states that mass cannot be created or destroyed during a chemical reaction. Therefore, the total mass of the reactants must be equal to the total mass of the products.
4. Since the total mass of the reactants is 4 u and the total mass of the products is 16 u, there is a difference of 12 u in mass.
5. According to Einstein's mass-energy equivalence principle (E = mc²), mass and energy are interchangeable. The energy released (Q) in the fusion reaction can be calculated using the equation:
Q = Δm × c²
Here, Δm represents the change in mass, and c is the speed of light, which is approximately 3 × 10^8 meters per second.
6. Plugging in the values, we have:
Q = 12 u × (3 × 10^8 m/s)²
Remember that 1 u is equivalent to 1.66 × 10^-27 kg.
7. To convert the units, we multiply by the conversion factor:
Q = (12 × 1.66 × 10^-27 kg) × (3 × 10^8 m/s)²
8. Performing the calculations, we find:
Q ≈ 2.7 × 10^-14 joules
Therefore, the energy released in the fusion reaction 2H + 2H → 4He + Q is approximately 2.7 × 10^-14 joules.