Answer:
The life time of the particle is [tex]2.491\times 10^{- 25} s[/tex]
Solution:
As per the question:
Average rest energy of [tex]Z^{0}boson = 91.19 GeV[/tex]
Uncertainty in rest energy, [tex]\Delta E_{r} = 2.5 GeV = 2.5\times 10^{9}\times 1.6\times 140^{- 19} J = 4\times 10^{- 10} J[/tex]
Now,
From the Heisenberg's Uncertainty Principle, we can write:
[tex]\Delta E_{r}\times \Delta T \geq \frac{h}{2\pi}[/tex]
where
T = Life time of the particle
[tex]\Delta T \geq \frac{h}{2\pi\Delta E_{r}}[/tex]
[tex]\Delta T \geq \frac{6.262\times 10^{- 34}}{2\pi\times 4\times 10^{- 10}}[/tex]
[tex]\Delta T \simeq 2.491\times 10^{- 25} s[/tex]
