Calculate the range of the force that might be produced by the virtual exchange of a proton.Assume ΔE⋅Δt = h/2π.(m_p = 1.67 × 10−²⁷ kg,c = 3.00 × 10⁸ m/s,and h/2π = 1.05 × 10−³⁴ J⋅s) A) 6.7 × 10−²⁵ m B) 2.1 × 10−¹⁶ m C) 6.0 × 10−⁸ m D) 1.5 × 10−¹⁵ m

Question

Quizplus · Accepted Answer

The range of the force can be calculated using the uncertainty principle:
ΔFΔt ≥ h/4πΔx
Assuming that the proton exchanging force is of the order of the electromagnetic force:
ΔF = 1/α*(e^2/4πεr^2) ≈ 10^-13 N
Where α is the fine structure constant, e is the elementary charge, and ε is the electric constant.
Substituting the values in the equation:
Δx ≥ h/4πΔFΔt
Δx ≥ (1.05 × 10^-34 J.s)/(4π(10^-13 N)(10^-22 s))
Δx ≥ 2.1 × 10^-16 m
Therefore, the correct answer is B) 2.1 × 10^-16 m.

Calculate the Range of the Force That Might Be Produced