What is the range and time period of this particle?

In summary: It is just a conceptual exercise. In summary, the residual strong interaction between nucleons is indirectly affected by a quark-antiquark pair and is mediated by a π-meson. The maximum time period in which this interaction takes place is 3.33 * 10-24 seconds, assuming it moves at a velocity of c. The range of the interaction is at least 7.07 * 10-16 meters, based on the Heisenberg uncertainty principle and the mass of the π-meson.
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Homework Statement


The longer-range inter-nucleon force is not a direct result of the gluon field, but is indirectly affected by a quark-antiquark pair (i.e. meson). If this ‘residual’ strong interaction between nucleons is mediated by a π-meson, then what is the maximum time period in which the interaction takes place? If we assume that it moves at a velocity v → c, then what is the range of the interaction? Show your working.

Homework Equations


Heisenberg uncertainty principle
E = mc2
distance = velocity * time

The Attempt at a Solution


ΔEΔt ≥ ħ/2
(mc2)Δt ≥ ħ/2
Δt ≥ ħ /( 2mc2)
d = vt →cΔt
cΔt ≥ ħ /(2mc)

∴ Range ≥ ħ /( 2mc)

mass of pion = 139.6 MeV/c2

Range ≥ 7.07 * 10-16 m (Range of π-meson)

Δt = d/c = 1*1015m / 3*108 m/s = 3.33 * 10-24s - maximum time range in which the interaction takes place
 
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  • #2
says said:
Range ≥ 7.07 * 10-16 m (Range of π-meson)
The direction of the inequality (≥) shows how problematic this approach is. It is not a minimal range obviously.
Anyway, it is the range scale, and probably the number the problem statement expects as "maximal" range.
Δt = d/c = 1*1015m / 3*108 m/s = 3.33 * 10-24s - maximum time range in which the interaction takes place
Why did you round the distance value here? Especially as you give three significant figures for the time afterwards.

The approach is fine.
 

1. What is the meaning of "range" in particle physics?

"Range" refers to the distance that a particle can travel before it loses its energy and interacts with another particle or medium.

2. How is the range of a particle determined?

The range of a particle is determined by its properties, such as its mass, charge, and energy, as well as the medium it is traveling through.

3. What is the time period of a particle?

The time period of a particle refers to the duration of its existence or decay. It is measured in units of time, such as seconds or milliseconds.

4. How is the time period of a particle calculated?

The time period of a particle is calculated by studying its decay rate and half-life, which is the time it takes for half of the particles in a sample to decay.

5. Can the range and time period of a particle change?

Yes, the range and time period of a particle can change depending on its energy, interactions with other particles, and the medium it is traveling through. These properties can also be altered through processes such as acceleration or decay.

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