# At how many femtometers does strong force cease to exist?

1. Jun 12, 2012

### Rorkster2

At 2.5 femtometer away from a quark the strong force is said to significantly loose power and become insignificant. At how many femtometers does the strong force completely loose any amount of tug?

2. Jun 12, 2012

### Staff: Mentor

As usual, there is no single point where it gets exactly 0. But the force is decreasing so quickly that it gets completely irrelevant (and small compared to the electromagnetic force, for example) just some femtometers away.

3. Jun 12, 2012

### Rorkster2

Ok. Is their any known way to find out the rate in which the force drops off? I.e. an equation of some sort?

4. Jun 12, 2012

### The_Duck

Someone may correct me on this, but I think for long distances it should fall off roughly like exp(-r/r0)/r, where r0 is the Compton wavelength of the pion, which is about 1.5 femtometers.

5. Jun 12, 2012

### Rorkster2

@The_Duck I looked that up to find out what it ment and google didn't return anything.

6. Jun 12, 2012

### The_Duck

In case the problem is notation, it means that at a distance r the strength of the strong force should be proportional to the function

$$\frac{e^{-r/r_0}}{r}$$

where r0 is 1.5 femtometers. Here's a plot of this behavior: http://www.wolframalpha.com/input/?i=plot+exp(-r/1.5)/r,+r=0..10
In the plot, the x axis is the distance in femtometers and the y axis is proportional to the strength of the strong force

7. Jun 12, 2012

### Rorkster2

Ahh thanks a lot. In the graph the x axis is length in femtometers and would Y be the strength? I'm pretty sure I get it I just want to be sure

8. Jun 12, 2012

### The_Duck

Yes. Just keep in mind that the numbers on the y axis don't mean anything; it's the shape of the graph that is meaningful.

9. Jun 12, 2012

### Rorkster2

You have rightfully earned the title the duck. Thank you