Question

A virtual particle having an approximate mass of 1014 GeV/c² 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)?

a) 1.05×10 −²⁴s
b) 2.10×10−²⁴s
c) 3.15×10−²⁴s
d) 4.20×10−²⁴s

Answer 1

According to the Heisenberg uncertainty principle, a virtual particle with a mass of 1014 GeV/c² can exist temporarily violating the conservation of mass-energy. The time for which it can exist can be calculated using the formula Δt = h / ΔE, where h is Planck's constant and ΔE is the uncertainty in energy.

Step-by-step explanation:

According to the Heisenberg uncertainty principle, temporary violation of the conservation of mass-energy is allowed. A virtual particle with a mass of 1014 GeV/c² can exist for a certain length of time. The uncertainty principle states that the uncertainty in energy, ΔE, multiplied by the uncertainty in time, Δt, should be greater than or equal to Planck's constant, h. Therefore, we can calculate the time for which the virtual particle can exist using the formula Δt = h / ΔE.

Given that the approximate mass of the virtual particle is 1014 GeV/c², the uncertainty in energy, ΔE, is equal to the mass of the particle, which is 1014 GeV/c². Substituting these values into the formula, we get Δt = h / 1014 GeV/c².

Using the value of Planck's constant, h = 6.62607015 × 10^-34 J·s, we can convert it to the appropriate units and calculate Δt.