What is the range and time period of this particle?

[says]

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 = mc²
distance = velocity * time

The Attempt at a Solution

ΔEΔt ≥ ħ/2
(mc²)Δt ≥ ħ/2
Δt ≥ ħ /( 2mc²)
d = vt →cΔt
cΔt ≥ ħ /(2mc)

∴ Range ≥ ħ /( 2mc)

mass of pion = 139.6 MeV/c²

Range ≥ 7.07 * 10^-16 m (Range of π-meson)

Δt = d/c = 1*10¹⁵m / 3*10⁸ m/s = 3.33 * 10^-24s - maximum time range in which the interaction takes place

 

[mfb]

Range ≥ 7.07 * 10^-16 m (Range of π-meson)

The direction of the inequality (≥) shows how problematic this approach is. It is not a minimal range obviously.
Anyway, it is the range scale, and probably the number the problem statement expects as "maximal" range.

Δt = d/c = 1*10¹⁵m / 3*10⁸ m/s = 3.33 * 10^-24s - maximum time range in which the interaction takes place

Why did you round the distance value here? Especially as you give three significant figures for the time afterwards.

The approach is fine.