Range of the Weak Force Use the masses of the weak-force mediators to estimate the range of the weak force. ORGANIZE AND PLAN Equation 26.2 relates particle mass m and interaction range R: m = h/2πRc

Question

Range of the Weak Force

Use the masses of the weak-force mediators to estimate the range of the weak force.

ORGANIZE AND PLAN Equation 26.2 relates particle mass m and interaction range R:

[latex]m=\frac{h}{2 \pi R c}[/latex] (Mass of force-mediating particle; SI unit: kg) (26.2).

[latex]m=\frac{h}{2 \pi R c}[/latex].

[latex] ext { Known: Rest energies } m_{ W ^{+}}{ }^{2}=m_{ W ^{-} c^{2}}=80.4 GeV ; m_{Z^{0}} c^{2}=[/latex] 91.2 GeV.

Accepted Answer

We first convert rest energies into masses, so we can work in SI units. From Chapter 25, you know the conversion factor [latex]1 u \cdot c^{2}=931.5 MeV =0.9315 GeV ext {. Converting the } W ^{+} ext {and } W ^{-} ext {rest }[/latex] energy:

[latex]\frac{80.4 GeV }{c^{2}} imes \frac{1 u \cdot c^{2}}{0.9315 GeV } imes \frac{1.661 imes 10^{-27} kg }{1 u }=1.43 imes 10^{-25} kg[/latex].

Thus the range of the weak interaction mediated by a W particle is approximately

[latex]R=\frac{h}{2 \pi m c}=\frac{6.626 imes 10^{-34} J \cdot s }{2 \pi\left(1.43 imes 10^{-25} kg ight)\left(3.00 imes 10^{8} m / s ight)}[/latex].

[latex]=2.46 imes 10^{-18} m[/latex].

[latex] ext { A similar calculation for the more massive } Z^{0}[/latex] particle gives a slightly smaller range:

[latex]R=2.16 imes 10^{-18} m[/latex].

REFLECT The weak force has an extremely short range. This makes sense physically, given that the beta decay takes place within a single nucleon.

Question 26.3: Range of the Weak Force Use the masses of the weak-force med...

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