1. The problem is based uponYukawa's original prediction for pion mass-energy.(adsbygoogle = window.adsbygoogle || []).push({});

suppose the force between nucleons is due to the emission of a particle mass m from one nucleon and the absorption by another. given the range of the nuclear force is

R=(1.4)[tex]\times[/tex]10[tex]^{-15}[/tex]

use [tex]\Delta[/tex]E[tex]\Delta[/tex]t ~ h bar

to make an order of magnitude estimate of the mass energy in MeV

2

x=position

p=momentum

E=energy

m=pion rest mass

h bar = reduced planck constant

t=time

c=speed of light

[tex]\Delta[/tex]=uncertainty in _

the equation required by the question is

[tex]\Delta[/tex]E[tex]\Delta[/tex]t ~ h bar

i also attempted using

E[tex]^{2}[/tex]=p[tex]^{2}[/tex]c[tex]^{2}[/tex] +m[tex]^{2}[/tex]c[tex]^{4}[/tex]

and the momentum form of the uncertainty principle

[tex]\Delta[/tex]p[tex]\Delta[/tex]x ~ h

I was pretty stumped because i couldn't fathom what the delta t represented, and how to use the required equation with just one variable. i used dimensional analysis as i knew it would have to be made up of constants h and c and the given value R (taken to be delta x) and got

E~[tex]\frac{hc}{R}[/tex]

But this does not take into account any prefactors and doesn't use the required equation. i also tried subbing the momentum form of the uncertainty principle into thye relativistic energy equation, but to no avail as the Delta t is still there

This is one of the first questions from my introductory quantum mech. course, so i'm not particularly clue up on the physical principle, can someone please point me in the right direction?

Help!

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# Homework Help: Estimating Pion mass using the uncertainty principle

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