Answer to Question #101098 in Quantum Mechanics for JAI SHREE RAAM

Question

Nuclear forces are mediated by exchange of pi-mesons of REST MASS 140 Mev .
using HEISENBERG UNCERTAINTY principle ,estimate the range OF Nuclear forces.

Answer 1

Using uncertainty principle in this form

$$\Delta E \Delta t\backsim \hbar$$

where

$\Delta E=140MeV; \Delta t=\frac {r}{c}$; r - range; c - light velocity

The range of nuclear forces

$$r\backsim \frac{\hbar c}{\Delta E }$$ $$r\backsim \frac{6.58\cdot 10^{-16}\cdot 3\cdot 10^8}{140\cdot 10^6}=0.141\cdot10^{-14} (m)=1.41\cdot 10^{-13} (cm)$$