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Chapter 6: Q6E (page 1519)

Estimate the range of the force mediated by an \({\omega ^0}\) g meson that has mass \(783\;MeV/{c^2}\) .

Short Answer

Expert verified

The range of the force is 1.26×10-16 m.

Step by step solution

01

Definition of force

The term force may be defined as the product of mass and acceleration.

02

Determine the range of force

The mass of theω0 particle is783 MeV/c2, and the minimum uncertainty energy is:

role="math" localid="1668318864281" ΔE=783 MeV(1.60×10-13 J/MeV)ΔE=1.25×10-10 J

The lifetime δtof the particle, according to the Heisenberg uncertainty principle:

δt=h2ΔEδt=1.055×10−34J⋅s21.25×10−10Jδt=4.21×10−25s

If we consider the speed of light is the average speed of the particle than

r−cδtr=3×108m/s4.21×10−25sr=1.26×10−16m

Hence, the range of the force is 1.26×10-16 m.

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