The attractive force between protons and neutrons in the nucleus is brought about by the exchange of a virtual pi-meson (m _$\pi$ = 140 MeV/c²).Estimate the longest time a virtual $\pi$⁰ can exist,in accordance with the uncertainty principle $\Delta E \Delta t = \hbar / 2$ .(1 eV = 1.6 *10 ^- ¹⁹ J. ) A)2.4 *10 ^- ²⁴ s B)6.9 *10 ^- ²⁷ s C)3.3 * 10 ^- ¹⁸ s D)2.4 *10 ^- ²¹ s E)1.6 *10 ^- ¹⁹ s

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Quizplus · Accepted Answer

The uncertainty principle states that the product of the uncertainty in energy and the uncertainty in time is greater than or equal to Planck's constant divided by 2. In this case, the uncertainty in energy is the mass of the virtual pi-meson, which is 140 MeV/c^2. The uncertainty in time is the lifetime of the virtual pi-meson, which we want to find.Plugging these values into the uncertainty principle, we get:140 MeV/c^2 * Δt ≥ ħ/2Solving for Δt, we get:Δt ≥ ħ/2 * 140 MeV/c^2Plugging in the values for ħ and c, we get:Δt ≥ (1.0545718 × 10^-34 J s) / (2 * 140 × 1.6 × 10^-13 J)Δt ≥ 2.4 × 10^-24 sTherefore, the longest time a virtual pi-meson can exist is 2.4 × 10^-24 s.

The Attractive Force Between Protons and Neutrons in the Nucleus π\piπ

The Attractive Force Between Protons and Neutrons in the Nucleus $\pi$