Question

Does the decay process \(n \rightarrow p+\pi^{-}\) violate any conservation rules?

Short answer

Answer: The decay process \(n \rightarrow p+\pi^{-}\) violates mass-energy conservation.

Step-by-step solution

Identify particles involved in the decay process

First, we need to identify the particles involved in the decay process, \(n \rightarrow p+\pi^{-}\), and their properties. In this case, we have a neutron (n) decaying into a proton (p) and a negatively-charged pion (\(\pi^{-}\)).

Determine properties for each particle

We need to determine the mass-energy, charge, spin, and baryon number for each particle. - Neutron (n): Mass-energy = 939.6 MeV, charge = 0, spin = 1/2, baryon number = 1 - Proton (p): Mass-energy = 938.3 MeV, charge = +1, spin = 1/2, baryon number = 1 - Negatively charged pion (\(\pi^{-}\)): Mass-energy = 139.6 MeV, charge = -1, spin = 0, baryon number = 0

Check charge conservation

Charge conservation states that the total charge before and after the decay process should be the same. In this case, we have: Charge Before Decay: Neutron charge = 0 Charge After Decay: Proton charge + Pion charge = (+1) + (-1) = 0 Since the total charge before and after the decay is the same, this decay process conserves charge.

Check spin conservation

Spin conservation states that the total spin quantum number before and after the decay process should be the same. In this case, we have: Spin Before Decay: Neutron spin = 1/2 Spin After Decay: Proton spin + Pion spin = (1/2) + 0 = 1/2 Since the total spin before and after the decay is the same, this decay process conserves spin.

Check mass-energy conservation

Mass-energy conservation states that the total mass-energy before and after the decay process should be the same. In this case, we have: Mass-energy Before Decay: Neutron mass-energy = 939.6 MeV Mass-energy After Decay: Proton mass-energy + Pion mass-energy = 938.3 MeV + 139.6 MeV = 1077.9 MeV Since the total mass-energy before and after the decay is not the same, this decay process does not conserve mass-energy.

Check baryon number conservation

Baryon number conservation states that the total baryon number before and after the decay process should be the same. In this case, we have: Baryon Number Before Decay: Neutron baryon number = 1 Baryon Number After Decay: Proton baryon number + Pion baryon number = 1 + 0 = 1 Since the total baryon number before and after the decay is the same, this decay process conserves baryon number.

Conclusion

The decay process \(n \rightarrow p+\pi^{-}\) conserves charge, spin, and baryon number. However, it does not conserve mass-energy. Therefore, this decay process violates mass-energy conservation and is not allowed.