Calculate the maximum wavelength of one of the photons produced when a proton and antiproton annihilate each other.

Sure, here are the steps to calculate the maximum wavelength of one of the photons produced when a proton and antiproton annihilate each other:

1. First, we need to calculate the total energy released when a proton and an antiproton annihilate each other. This is given by Einstein's equation E=mc^2, where m is the mass of the proton (or antiproton, since they have the same mass), and c is the speed of light. The mass of a proton is approximately 1.67 x 10^-27 kg, and the speed of light is approximately 3 x 10^8 m/s. So, the energy released is E = (1.67 x 10^-27 kg) * (3 x 10^8 m/s)^2 = 1.503 x 10^-10 Joules.

2. This energy is carried away by two photons (since charge, baryon number, lepton number, etc. must be conserved), so each photon carries away half of this energy, which is 1.503 x 10^-10 Joules / 2 = 7.515 x 10^-11 Joules.

3. The energy of a photon is given by the equation E=hf, where h is Planck's constant (approximately 6.626 x 10^-34 Joule seconds), and f is the frequency of the photon. We can rearrange this equation to solve for the frequency: f = E/h = (7.515 x 10^-11 Joules) / (6.626 x 10^-34 Joule seconds) = 1.134 x 10^23 Hz.

4. The wavelength of a photon is given by the equation λ=c/f, where λ is the wavelength, c is the speed of light, and f is the frequency. Plugging in the values we have, we get λ = (3 x 10^8 m/s) / (1.134 x 10^23 Hz) = 2.645 x 10^-16 m.

So, the maximum wavelength of one of the photons produced when a proton and antiproton annihilate each other is approximately 2.645 x 10^-16 meters.