How much energy (in MeV) is released in the reaction proton + deuteron goes to 3He + gamma? (You may ignore the initial kinetic energy of the reactants.)
For the purposes of this problem, use the following masses (in MeV/c2):
Proton: 938.783263054
Neutron: 939.5657182828
Deuteron: 1876.12457290064
3H: 2809.43251234168
3He: 2809.41388245528
To calculate the energy released in the given reaction, we need to calculate the mass difference before and after the reaction and convert it into kinetic energy using Einstein's famous equation E = mc². Here are the steps to find the energy released:
1. Calculate the initial mass before the reaction. In this case, it is the sum of the masses of the proton and deuteron:
Initial mass = Mass of proton + Mass of deuteron
2. Calculate the final mass after the reaction. It is the sum of the masses of 3He and the gamma particle:
Final mass = Mass of 3He + Mass of gamma
3. Calculate the mass difference:
Mass difference = Final mass - Initial mass
4. Convert the mass difference into energy using the equation E = mc²:
Energy released = Mass difference × c²
Now, let's plug in the given values and calculate the energy released:
1. Initial mass:
Mass of proton = 938.783263054 MeV/c²
Mass of deuteron = 1876.12457290064 MeV/c²
Initial mass = 938.783263054 MeV/c² + 1876.12457290064 MeV/c²
Initial mass = 2814.90783595464 MeV/c²
2. Final mass:
Mass of 3He = 2809.41388245528 MeV/c²
Mass of gamma particle = 0 MeV/c² (assuming it has no mass)
Final mass = 2809.41388245528 MeV/c² + 0 MeV/c²
Final mass = 2809.41388245528 MeV/c²
3. Mass difference:
Mass difference = Final mass - Initial mass
Mass difference = 2809.41388245528 MeV/c² - 2814.90783595464 MeV/c²
Mass difference = -5.49395349936 MeV/c²
4. Energy released:
Energy released = Mass difference × c²
Energy released = -5.49395349936 MeV/c² × c²
Energy released = -5.49395349936 MeV
Note: The negative sign indicates that energy is released in the reaction.
So, the calculated energy released in the given reaction is approximately -5.494 MeV.