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## Homework Statement

The longer-range inter-nucleon force is not a direct result of the gluon field, but is indirectly affected by a quark-antiquark pair (i.e. meson). If this ‘residual’ strong interaction between nucleons is mediated by a π-meson, then what is the maximum time period in which the interaction takes place? If we assume that it moves at a velocity v → c, then what is the range of the interaction? Show your working.

## Homework Equations

Heisenberg uncertainty principle

E = mc

^{2}

distance = velocity * time

## The Attempt at a Solution

ΔEΔt ≥ ħ/2

(mc

^{2})Δt ≥ ħ/2

Δt ≥ ħ /( 2mc

^{2})

d = vt →cΔt

cΔt ≥ ħ /(2mc)

∴ Range ≥ ħ /( 2mc)

mass of pion = 139.6 MeV/c

^{2}

Range ≥ 7.07 * 10

^{-16}m (Range of π-meson)

Δt = d/c = 1*10

^{15}m / 3*10

^{8}m/s = 3.33 * 10

^{-24}s - maximum time range in which the interaction takes place