Chapter 6: Q6E (page 1520)

Estimate the range of the force mediated by an $ω^{0} g$ meson that has mass $783 MeV / c^{2}$ .

Short Answer

Expert verified

The range of the force is $1.26 \times 10^{- 16} m$ .

Step by step solution

Definition of force

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

Determine the range of force

The mass of the $ω^{0}$ particle is $783 MeV / c^{2}$ , and the minimum uncertainty energy is:

$Δ E = 783 MeV (1.60 \times 10^{- 13} J / MeV)$

$Δ E = 1.25 \times 10^{- 10} J$

The lifetime $δ t$ of the particle, according to the Heisenberg uncertainty principle:

$δ t = \frac{h}{2 Δ E}$

$δ t = \frac{1.055 \times 10^{- 34} J \cdot s}{2 (1.25 \times 10^{- 10} J)}$

$δ t = 4.21 \times 10^{- 25} s$

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

$r = c δ t r = (3 \times 10^{8} m / s) (4.21 \times 10^{- 25} s) r = 1.26 \times 10^{- 16} m$

Hence, the range of the force is role="math" localid="1663932465949" $1.26 \times 10^{- 16} m$ .

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Estimate the range of the force mediated by an $ω^{0} g$ meson that has mass $783 MeV / c^{2}$ .

Short Answer

Step by step solution

Definition of force

Determine the range of force

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Estimate the range of the force mediated by an ω0gmeson that has mass 783MeV/c2.

Short Answer

Step by step solution

Definition of force

Determine the range of force

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Circular Motion and Gravitation

Further Mechanics and Thermal Physics

Electricity and Magnetism

Work Energy and Power

Nuclear Physics

Study anywhere. Anytime. Across all devices.

Estimate the range of the force mediated by an $ω^{0} g$ meson that has mass $783 MeV / c^{2}$ .