Final answer:
The uncertainty in the energy released in the decay of a π⁰ due to its short lifetime can be determined using theHeisenberg uncertainty principle. It is given by ℏ/τ.
Step-by-step explanation:
The uncertainty in the energy released in the decay of a π⁰ due to its short lifetime can be determined using the Heisenberg uncertainty principle. The energy-time uncertainty relation in quantum mechanics states that the uncertainty in the energy (ΔE) is inversely proportional to the uncertainty in time (Δt). Mathematically, ΔE × Δt ≥ ħ/2, where ħ is the reduced Planck's constant.
Since the π⁰ particle has a short lifetime (denoted by τ), we can express the uncertainty in time as τ. Therefore, the uncertainty in energy (ΔE) can be represented as ħ/τ. Hence, the correct option is (a) ℏ/τ.