Lowest possible energy of neutron?

Question

Estimate the lowest possible energy of a neutron contained in a typical nucleus of radius 1.14E-15 m.

I am totally stuck on this question. Every equation I have found seems to be in reference to an electron. I don't need the answer given to me...but a push in the right direction would be much appreciated!

Answer 1

When doing an energy problem, start by doing an energy audit for the system. The goal is to find the system's (neutron) total energy, which, from the conservation of energy, will remain fixed no matter what state the system is in.

There are three kinds of energy when auditing: kinetic (KE), potential (PE), and work (WE). KE results when the system is in motion (like a vibrating neutron might be). KE usually results when work (WE) is done to convert potential energy into KE. Sub atomic particles tend to have jitter; so I'd think a neutron would be vibrating no matter where it is in the nucleus.

PE results in work being done on the system (neutron) to put it into a higher potential state. For example, when we lift a mass m to a height h, we do WE = mgh work against gravity g. And that WE becomes PE = mgh, the potential of the mass to create kinetic and other kinds of energy (like heat).

In the case of a neutron on the edge (R = 1.14 X 10^-15 m) of a nucleus, I would think that PE(R) > PE(0) which would be the potential energy of a neutron near the center. [I think this because PE = mgh = 0 if h = 0.] That potential would come from working against the strong and weak atomic forces. So you'd need to find out how PE varies with the position of a neutron under the strong and weak forces.

Once you've done the audit, you can move the neutron around within the nucleus to see how KE and PE might vary to keep its total energy TE = constant, which it would do according to the conservation of energy. Watch out for WE, work done on or by the neutron, as you move it about, however. While that would not change the TE it would change if the neutron had all that TE or not.

For example, if a block of wood slides down a ramp, some of the TE it had before sliding will convert into KE at the bottom, but some of it will also become heat due to the work the block has to do against friction. So that work is lost by the block and its KE will be less than it would otherwise be without the friction. The point is, when looking at the neutron from point to point in the core, watch out for WE due to some sort of "friction" or similar.

PS: Don't forget PE(m) = mc^2; where m is the mass of the neutron. That is, some of the TE is potential energy from the mass energy equivalency. So you have it plus the positional PE(R) to look at for potential energy.

Answer 2

The equation shows that a very small anount of matter can be "converted" to an incredible amount of energy, and that matter contains this energy . The fact that the speed of light squared is a HUGE number, multiplied by mass of any amount other than zero, shows us the amount of energy contained in the matter.

Answer 3

Delve into the strong force.

Answer 4

im not sure, but this answers helped me out in moments like this before
so ill say, its the planck energy.