Final answer:
The question asks how much energy is produced when 1.3 kilograms of protons is converted into energy through a nuclear reaction using E = mc². To calculate this, we first determine the number of protons in 1.3 kg and then apply Einstein's equation to find that the energy released is 1.17 x 10^17 joules.
Step-by-step explanation:
The mass of 1 proton is approximately 1.67 x 10^-27 kilograms. If 1.3 kilograms of protons are converted into energy, we can calculate the amount of energy produced using Einstein's equation E = mc², where E represents energy, m is mass, and c is the speed of light in a vacuum (approximately 3.00 x 10^8 meters per second).
To find the energy produced, we first calculate the number of protons in 1.3 kilograms:
- Number of protons = Total mass / Mass of one proton
- Number of protons = 1.3 kg / (1.67 x 10^-27 kg/proton)
- Number of protons = 7.78 x 10^26 protons
Now, using E = mc²:
- E = (1.3 kg) x (3.00 x 10^8 m/s)²
- E = 1.3 kg x 9 x 10^16 m²/s²
- E = 1.17 x 10^17 joules
This energy is the amount produced if 1.3 kilograms of protons were completely converted into energy during a nuclear reaction.