Calculating the Density of a Neutron

[FeDeX_LaTeX]

Hi, I did some calculations and I worked out the density of 1 neutron to be about 3.19887549*10^57 kg/m^3. However, I want to know if the method I used is correct.

Density = mass/volume, correct?

If this is true, then

Density = [mass of neutron]/[volume of neutron]

I found the volume of a neutron by modelling it as a sphere, with volume (4/3)pi*r^3. The calculation I ended up doing was;

(1.67492729*(10^27))/(4/3 * pi*((10^-10)/2)^3) = 3.19887549*10^57 kg/m^3

Where the 1.67492729 is the mass of a neutron (source: wikipedia).

Is my working correct?

Cheers

 

[mathman]

The method is correct, but where did you get r?

 

[Glen Bartusch]

The method is correct, but where did you get r?

It really doesn't matter, since Warner Heisenberg already showed us that when the quantity of one non-commuting variable is known in the subatomic particle, the other variable of that particle becomes uncertain (Heisenberg's uncertainty principle).

 

[netheril96]

I personally think the neutron's radius is unknown yet
And since we always regard neutron as a point,its density is useless
We need only its mass

 

[Glen Bartusch]

I personally think the neutron's radius is unknown yet
And since we always regard neutron as a point,its density is useless
We need only its mass

Agreed. I'd also like to add that we need know also the neutron's energy (in electron-volts, of course), as well as its spin.

 

[Vanadium 50]

1.67492729*(10^27)

1.67492729 x 10^²⁷ is most certainly not the mass of the neutron. Check again,.

And since we always regard neutron as a point

No we don't. The neutron has a measured radius. Of course, it's boundary is not sharp, but you could say that about many things that have a published radius: a gold atom, the planet Jupiter, the asteroid belt.

 

[Matterwave]

10^-10 is more like the radius of an atom (where the electron likes to hang out). It's not the radius of the Neutron...but I suppose you could use that as an upper bound. (Nuclei are more on the order of 10^-15m in radius)