Final answer:
The mass in GeV/c² of a virtual carrier particle with a range limited to 10⁻³⁰ m by the Heisenberg uncertainty principle is approximately 1.178 x 10^19 GeV/c².
Step-by-step explanation:
To calculate the mass in GeV/c² of a virtual carrier particle with a limited range, we can use the Heisenberg uncertainty principle. According to the principle, the uncertainty in position (Δx) and the uncertainty in momentum (Δp) are inversely related. Mathematically, this can be expressed as: ΔxΔp ≥ h/4π, where h is the Planck constant.
In this problem, the range (Δx) is given as 10⁻³⁰ m. Since the momentum can be related to mass and velocity as: p = mv, we can rewrite the Heisenberg uncertainty principle as: ΔxΔmv ≥ h/4π.
We can now calculate the mass by rearranging the equation: m = Δp/Δv = (h/4πΔx)/Δv. Since the range is given in meters and the speed of light (c) is approximately 3 x 10^8 m/s, the velocity can be calculated as Δv = c/Δx.
Substituting the values, we get: m = (h/4πΔx)/(c/Δx) = h/(4πc), where h = 6.626 x 10^-34 J s and c = 3 x 10^8 m/s.
Plugging in the values, we get: m ≈ (6.626 x 10^-34 J s)/(4π x 3 x 10^8 m/s) = 1.178 x 10^19 J/C² = 1.178 x 10^19 GeV/c².