A virtual particle having an approximate mass of \[{\rm{1}}{{\rm{0}}^{{\rm{14}}}}{\rm{GeV/}}{{\rm{c}}^{\rm{2}}}\]may be associated with the unification of the strong and electroweak forces. For what length of time could this virtual particle exist (in temporary violation of the conservation of mass-energy as allowed by the Heisenberg uncertainty principle)?

The Uncertainty Principle of Heisenberg states that it is impossible to precisely compute energy transferred and the time taken simultaneously. There will at least be an uncertainty equal toh/4π . Here, h is Plank’s constant.

Mass of the particle is m = 10¹⁴MeV/c².

Using the uncertainty equation as a guide,

\[{\rm{\Delta E\Delta t = }}\frac{{\rm{h}}}{{{\rm{4\pi }}}}\],

we can get the duration of existence\[\left( {{\rm{\Delta t}}} \right)\]and uncertainty in energy\[{\rm{\Delta E = \Delta m}}{{\rm{c}}^{\rm{2}}}\]

\[\begin{array}{c}\Delta t = \frac{h}{{4\pi \Delta m{c^2}}}\\ = \frac{{\left( {6.63 \times {{10}^{ - 34}}\;{\rm{J}}{\rm{.s}}} \right)}}{{4\pi \times \left( {{{10}^{14}} \times {{10}^9} \times 1.6 \times {{10}^{ - 19}}\;{\rm{kg}}} \right)}}\\ = 3.3 \times {10^{ - 39}}\;{\rm{s}}\end{array}\]

Therefore,this particle exists for \[3.3 \times {10^{ - 39}}\;{\rm{s}}\]