One possible energy source for the mysterious object you've just discovered is the fusion of hydrogen to form carbon-12 (the most common and stable isotope of Carbon). Hydrogen has an atomic mass of 1.00794 u, while carbon has an atomic mass of 12.010 u.
If you fuse Hydrogen to carbon, what percentage of the original mass is converted into energy?
To determine the percentage of the original mass converted into energy during the fusion of hydrogen to form carbon-12, you need to calculate the mass difference before and after the fusion reaction. Let's perform the calculations step by step.
1. Determine the initial mass of the reactants:
- For hydrogen (H), the atomic mass is 1.00794 u.
- For carbon-12 (C), the atomic mass is 12.010 u.
2. Calculate the initial total mass by adding the individual masses:
initial mass = mass of hydrogen + mass of carbon
initial mass = 1.00794 u + 12.010 u
3. Determine the final mass of the products:
- Carbon-12 has an atomic mass of 12.010 u.
4. Calculate the mass difference by subtracting the final mass from the initial mass:
mass difference = initial mass - final mass
5. Convert the mass difference to energy using Einstein's mass-energy equivalence equation (E = mc²), where c is the speed of light (approximately 3.0 x 10^8 m/s):
energy released = mass difference x (speed of light)²
6. Finally, calculate the percentage of the original mass converted into energy:
percentage = (energy released / initial mass) x 100
By following these steps and performing the necessary calculations, you can determine the percentage of the original mass that is converted into energy during the fusion of hydrogen to form carbon-12.