# Why is energy of emitted particles negative?

recently I had one problem here, and in comments I got interesting thing written by user Sofia. Unfortunetly, the topic is in hold now and I can't ask her more.

Here is the comment:

Radio-activity would help? Your class heard - I suppose - of substances as Uranium, Plutonium, and others, that emit electrons, alpha-particles., etc. But the nuclei of these atoms create an electric field around themselves, and the potential energy of this field is much higher tan the total energy of the emitted particle. We know that equality: total energy = kinetic energy + potential energy. So, the non-Newtonian behavior is that when passing through this field, the kinetic energy of the emitted particles is NEGATIVE.

Why is it negative?

Thanks!

## 1 Answer

KInetic energy is never negative, the answer you got was wrong. Of course, you could say methaporically that when the particle is tunneling the KE is negative, but that cannot be measured, and as far as I know, the particle that tunnels is either on one side or the other of the barries, but never inside. In quantum theory the eigenvalues of kinetic energy cannot be negative. The apparent violation can be explained by the uncertainty principle, where the particle borrow energy from the vacumm for a short persiod of time so it can cross the barrier, but by the same reason the particel cannot be measured while in a state of borrowed energy.

• Thanks for clearing that. Do you have any ideas where do Newton's Laws not work, I mean practical things. It's high school work, so you can neglect a lot of things. For example why do photons have momentum when they have 0 mass (I neglect rest mass) – Serpentes Nov 27 '14 at 16:28
• Sure, in both special and general relativity newton's law do not work. Neither in quatum mechanics. Actually Newtons law's are only a good approximation whenever you either have: low speeds, low gravity, or the motion of macroscopic objects that do not display quantum effects. – Wolphram jonny Nov 27 '14 at 16:32
• your example of the photon is an example of special relativity, but also quantum mechanics. You probably should post this as a different question "where do Newton's Laws not work" if you want examples of that. My guess is you will get many interesting answers and examples. – Wolphram jonny Nov 27 '14 at 16:34
• So on very low mass (atoms and subatomic particles) do NL not work? Can you name any practical cases where do they not work? – Serpentes Nov 27 '14 at 16:39
• @user3932494: This is a deeper question than you realize. Newton's laws don't work in a lot of situations and work only approximately in others. But a (very) short answer is that you can't use Newton's laws when things are very small (like atoms), very heavy (like black holes), or very fast (like particles in an accelerator). – Javier Nov 27 '14 at 16:44