2. With uncertainty in determining the energy Delta E=10^-15 I, a particle can exist a time as (s): 5) 10^- 1) 10^-18 20 2) 10^-19 3) 10^-15 4) 10^-10

To determine the time a particle can exist given the uncertainty in energy, we can use the Heisenberg Uncertainty Principle. The principle states that the product of the uncertainties in position and momentum is on the order of Planck's constant divided by 4π:Δx * Δp ≥ ħ / 2However, in this case, we are given the uncertainty in energy (ΔE) instead of the uncertainty in momentum (Δp). We can use the relationship between energy and time to find the uncertainty in time:ΔE * Δt ≥ ħ / 2Given that ΔE = 10^-15 eV, we can rearrange the equation to solve for Δt:Δt ≥ ħ / (2 * ΔE)Using the value of Planck's constant (ħ) as 1.05 × 10^-34 J·s and converting the energy from eV to Joules (1 eV = 1.6 × 10^-19 J), we can calculate the uncertainty in time:Δt ≥ (1.05 × 10^-34 J·s) / (2 * 10^-15 eV * 1.6 × 10^-19 J/eV)Δt ≥ 3.25 × 10^-19 sTherefore, the particle can exist for a time greater than or equal to 3.25 × 10^-19 seconds. The correct answer is:2)