Do they oscillate relative to each other? What is the frequency? What is the amplitude? I would think they oscillate since electrons move all over the place at high speeds and there is attractive Coulomb force between electrons and protons.
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1$\begingroup$ I understand you refer to the nuclear "reactions" $n^0 \to p^+ + \pi^-$ and $p^+ \to n^0 + \pi^+$, which transmutate identity of these nucleons. $\endgroup$– DaviusCommented Jun 30, 2022 at 10:35
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$\begingroup$ I don't, I was just asking if they oscillate, I was interested what the frequency of their oscillations would be if they do. I was wondering if any of the neutrons or the protons inside of an atom oscillate, that would require a periodic force to put them out of balance i was thinking this to be Coulomb force from electrons and protons, also a reinstituting force would be needed for example strong or weak force. Thanks for trying to understand my question, i was just wondering, my assumptions might be very dumb. $\endgroup$– RaleBjekaCommented Jun 30, 2022 at 10:58
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2 Answers
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Given that nucleon is bound to nuclei radius,- this per Heisenberg uncertainty, gives us uncertainty in nucleon speed, which is :
$$ \Delta v = \frac {ℏ}{2~m_n R_0 A^{1/3}} $$
Where $m_n$ is nucleon mass, $R_0 = 1.2×10^{−15}~m$ and $A$ is nucleon amount in specific atom.
If we would calculate speed uncertainty for neutron in Iron nucleus, this equation would give that such neutron would jiggle around with $ \approx 7000 \text {km/s} $ uncertainty in speed, which is quite high.
To get representation of neutron oscillation frequency, imagine that this speed is tangential speed of neutron revolving around nuclei, which is not quite a good model, but gives fast estimates. In this case you can use angular frequency and tangential speed relationship : $$ v_{_\perp} = \omega~r $$
to extrapolate neutron oscillation frequency order in Iron atom, which would be on the order $$ f \approx 10^{21}~\text{Hz} $$.
Which is amazingly huge. I can't say if this is true, but certainly nucleons in a nuclei aren't something hammered to exact position like raisins in a bread. They are more describable by a quantum wavefunction, which probably could be calculated to complete nuclei as well.
answered Jun 30, 2022 at 11:52
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Protons and neutrons in nuclei interact mainly via strong and weak forces, which is why the excitation energies of nuclei (i.e., the frequencies with which protons and neutrons "oscillate") are usually much bigger than those associated with electrons, which interact with protons via electromagnetic interaction (that is the Coulomb forces, strong, weak and Coulomb interactions are different kinds of fundamental interactions).
Thus, characteristically, the atomic spectra associated with movement of electrons lie in infrared, visible and sometimes X-ray region, whereas those of nuclei are in gamma-ray region (see also Do nuclei emit photons?).
