The strong force interaction between a proton and a neutron can be described by

Question

The strong force interaction between a proton and a neutron can be described by the exchange of a pion consisting of an up/anti-up pair of quarks. Since this uncharged pion flickers into existence from nothingness, it is called a 'virtual particle' and it woudl seem to violate teh fundamental law of conservaiton of energy. However, the Heisenberg uncertainty principle permits its existence as long as its lifetime is short enough. Estimate the lifespan of this virtual particle. Assume the rest mass of an up quark is to be 2.3 MeV/c^2

Explanation / Answer

Rest mass = 2.3 MeV/c^2

So, it's energy = Rest Mass * c^2

= 2.3MeV = 2.3 * 10^6 * 1.6 * 10^-19 J = 3.68 * 10^-13 J ~ uncertainity in energy

Now, uncertainity in Energy * uncertainty in time = h/4Pi

-> uncertainty in time = h/(4*Pi*uncertainty in Energy) = 1.439*10^-23 s ~ LIFETIME

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