If the radius of a neutron is 1x10-13 cm calculate the density of a neutron in g over cm3?

Answer 1

According to the question, the given only information is:

Radius of a neutron is 1*10^-13 cm

And the purpose is to:

Find out the density of a neutron in grams over cm^3

(So it's only one neutron?)

THE MOTHOD

Since we know the density of a certain object can be acquired by using the formula Density=Mass / Volume, now the only uncertainty is the mass of a neutron.

There is a way to estimate the mass of a neutron through an experiment, which will be needing the followings, a mass spectrometer, an electronic gun, alpha particle, a nitrogen particle.

INSTRUCTIONS

1) Use an electronic gun to shoot out an electron, into an orbit around the mass spectrometer. Magnetic force would equal to centripetal force, and by using this formula

eVB=m*(V^2/R)

we could find out the mass of an electron.

2) Collide an alpha particle with a nitrogen particle, to produce a proton. By using the same method above, calculate the mass of the proton with a mass spectrometer.

3) Collide an alpha particle with a nitrogen particle with a regulated energy so that the alpha particle could be scattered. By using the laws "Conservation of momentum" and "Conservation of energy", we could find out the mass of the nitrogen nucleus(M).

M=7*(mass of proton + mass of neutron)

A neutrons mass could be estimated by solving the equation above.

Thus the density of a neutron is

D=(1.674927*10^-27) grams/ 1cm^3=1.674927*10^-27 g/cm^3

CUBES

If the question were "If the radius of a neutron is 1*10^-13 cm, calculate the density of neutrons in g over cm3?", the method would be totally different and difficult, as well as controversial.

1) BLOCKS

Since the particle is neutron that we are taking into account, we could assume that neutrons can be positioned side by side with no space and force amongst them. Just like constructing a building, bricks and bricks are very close together, but rather than rectangulars, more sphere shaped perhaps.

D=M/V={[1 / (2*1*10^-13)]^3*1.674927*10^-27} grams/ 1 cm^3=2.09365875*10^11

Whcih is not possible.

2) LATTICE

Maybe neutrons could be placed in a way like NaCl or other solids(if possible), with a distance between one another. This is where math comes into place. Note that there are three forms of lattace, which means three different ways of calculation and results.

Anyways, this question is still a bit odd. We might be asking the dencity of a lattice which NaCl forms, but not possibly the density of neutrons, unless under special circumstances.