Calculate the uncertainty in energy of an unstable elementary particle that has an average life time of 7.2 * 10 ^ - 9 * s

To calculate the uncertainty in energy of an unstable elementary particle, we can use Heisenberg's Uncertainty Principle. The principle states that the uncertainty in energy (ΔE) and the uncertainty in time (Δt) are related by the equation:

ΔE * Δt ≥ h/4π

where h is Planck's constant (6.62607015 × 10^-34 m^2 kg / s).

Given that the average lifetime of the particle is 7.2 * 10^-9 s, we can use this as our Δt. Plugging this into the equation gives us:

ΔE * (7.2 * 10^-9 s) ≥ (6.62607015 × 10^-34 m^2 kg / s) / 4π

Solving for ΔE gives us:

ΔE ≥ (6.62607015 × 10^-34 m^2 kg / s) / (4π * 7.2 * 10^-9 s)

Calculating the right side of the equation gives us:

ΔE ≥ 5.77 * 10^-26 J

So, the uncertainty in energy of the particle is at least 5.77 * 10^-26 Joules.