The process of fusing an electron and a proton to produce a neutron is known as electron capture. It involves the conversion of a proton into a neutron, accompanied by the emission of a neutrino.
To calculate the energy required for this process, we need to consider the mass difference between the initial particles (electron and proton) and the final particle (neutron). According to current understanding, the mass of a neutron is slightly greater than the combined mass of an electron and a proton.
The mass of an electron is approximately 9.10938356 × 10^-31 kilograms (kg), and the mass of a proton is approximately 1.6726219 × 10^-27 kg. The mass of a neutron is roughly 1.674927498 × 10^-27 kg.
The energy required to convert mass into energy is given by Einstein's famous equation, E = mc^2, where E is the energy, m is the mass difference, and c is the speed of light (approximately 299,792,458 meters per second).
To calculate the energy required for electron capture, we subtract the combined initial mass of the electron and proton from the final mass of the neutron:
Δm = (mass of neutron) - (mass of electron + mass of proton)
Δm = (1.674927498 × 10^-27 kg) - (9.10938356 × 10^-31 kg + 1.6726219 × 10^-27 kg)
Δm = 1.67331483 × 10^-31 kg
Using the equation E = mc^2, we can calculate the energy:
E = (1.67331483 × 10^-31 kg) × (299,792,458 m/s)^2
E ≈ 1.503 × 10^-14 joules (J)
So, the energy required to fuse an electron and a proton to produce a neutron through electron capture is approximately 1.503 × 10^-14 joules.