The strong nuclear interaction has a range of approximately 0.70 *10^-¹⁵ m.It is thought that an elementary particle is exchanged between the protons and neutrons,leading to an attractive force.Utilize the uncertainty principle $\Delta E \Delta t = \hbar / 2$ to estimate the mass of the elementary particle if it moves at nearly the speed of light. A)140 MeV/c²,a pion B)511 keV/c²,an electron C)96 GeV/c²,a Z boson D)500 MeV/c²,a K meson E)106 MeV/c²,a muon

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The uncertainty principle states that the product of the uncertainty in energy and the uncertainty in time must be greater than or equal to Planck's constant divided by 2. In this case, the uncertainty in time is approximately the time it takes for the elementary particle to travel the range of the strong nuclear interaction, which is approximately 0.70 x 10^-15 m. The uncertainty in energy is approximately the mass of the elementary particle times the speed of light. Therefore, the mass of the elementary particle must be greater than or equal to:$$\Delta E \Delta t = \hbar / 2$$$$m c^2 (0.70 x 10^-15 m) = \hbar / 2$$$$m = \frac{\hbar}{2 c^2 (0.70 x 10^-15 m)}$$$$m = 140 MeV/c^2$$This is the mass of a pion, which is an elementary particle that is exchanged between protons and neutrons in the strong nuclear interaction.

The Strong Nuclear Interaction Has a Range of Approximately 0 ΔEΔt=ℏ/2\Delta E \Delta t = \hbar / 2ΔEΔt=ℏ/2

The Strong Nuclear Interaction Has a Range of Approximately 0 $\Delta E \Delta t = \hbar / 2$