One of the mediators of the weak interaction is the Z^0 boson, which has a mass of 91 GeV / c^2

step 1 We have that the Z boson is a mediator of the weak interaction, and we want to know what is the

One of the mediators of the weak interaction is the Z^0...

One of the mediators of the weak interaction is the $\mathrm{Z}^{0}$ boson, which has a mass of $91 \mathrm{GeV} / c^{2} .$ Use this information to find an approximate value for the range of the weak interaction.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Mediator Particle Mass and Interaction Range

In quantum field theory, the mass of a mediator particle directly affects the range of the force it carries. The heavier the mediator, the shorter the distance over which the force can act. This relationship is a key reason why the weak interaction, mediated by massive particles, has a very short range compared to forces mediated by massless particles.

Compton Wavelength

The Compton wavelength, given by ?/(Mc), where ? is the reduced Planck constant, M is the mass of the particle, and c is the speed of light, provides an estimate of the quantum mechanical 'size' or effective range of a particle's influence. For a boson like the Z?, its Compton wavelength sets the scale for how far its mediated force can extend before becoming negligible.

Yukawa Potential

The Yukawa potential describes the interaction between particles mediated by massive bosons. It takes the form V(r) ? (e^(–r/?))/r, where ? is related to the mediator's Compton wavelength. This potential shows that the force decreases exponentially with distance, which is why forces like the weak interaction have a limited range due to the significant mass of their mediating particles.

Transcript

Please give Ace some feedback