Use the Heisenberg uncertainty principle to estimate the mass of the meson if the range of the nuclear force R_{N} is about 1 fm.
Strategy The uncertainty principle allows energy conservation to be violated during a short time Δt. We will let energy conservation be violated to the extent of the excess energy ΔE required to create the meson. The fastest speed possible for the meson is c, so the distance the meson travels in time Δt is c Δt. This distance c Δt must be about the range of the nuclear forceR_{N}.