Why did Rutherford's scattering experiment disprove the plum pudding? Assuming a gold-atom to be a large homogeneous ball and hitting it with small homogenuous $\alpha$-balls should lead to the actually observed scattering angle distribution, why would anyone assume that the $\alpha$-particles would go through the gold-atom (am I right that back then the idea was that the gold atom is indeed a more or less solid ball)?
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What stops one of the two following scenarios from happening, consistent with the plum pudding model?   The $\alpha$ particle, attracted by the electrons on the outer shell of the pudding, orbits nearly parabolically around the atom, causing the near-180 degree deflection angle seen. The $\alpha$ particle hits a plum pudding atom directly, and because the atom consists largely of positive charge, it is deflected by nearly 180 degrees.    Followup: did they know anything about the spacing of these plum-pudding atoms? Did they expect them to be lined up in a grid-like way; difficult to penetrate?  I am a physics undergraduate, I've only taken an intro QM class, it would be nice if that were kept in mind while answering.
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The  is a well-known and very useful tool for solving problems in electrostatics.  Unfortunately, when I was taught this method, it was presented simply as an algorithm. No real physical justification was given for its usage, and there was a complete absence of rigorous mathematics. The method has always been a little hazy to me since.  If someone could give a rigorous first-principles derivation of this method from Maxwell's equations (perhaps simply Coulomb's law?), it would be most appreciated.
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Using a "successive impact model" (as if each ball were seperated from the other ones), I produced the following animations:    You can see any combination of balls with masses of 1 or 2 (left) or 1 and 4 (right).  Unfortunately, I do not have any Newton cradle to make some experiments, and I'd like to compare my results with observations. I contacted the author of , which is the most instructive one I found about asymmetric Newton cradle. In particular, he writes that the "OoO" configuration behaves as the "ooo" one, which is not what I simulate. But the author is not sure whether who is wrong because he did the experiments a long time ago.  I am especially interested in asymmetric Newton cradle with simultaneous impacts: left and right balls collinding at the same time.   Please let me know if you have any idea on where to find such experimental data.  Edit Just of few general remarks to avoid extending the comments.    Energy and momentum are conserved. However, they are sufficient to ensure uniqueness of the post-impact velocities only when there are 2 balls. The successive impact model precisely consists in propagating the impact ball after ball, and therefore leads to a unique solution (which conserves momentum and energy globally). From the waves point of view, changing the mass of a ball can be done by increasing the diameter, or the density (or a combination of both). This simple model cannot account for such subtleties of course, but maybe it does not matter when the balls are "small enough". Even if I think it's quite basic, following WetSavannaAnimalakaRodVance's comment, I am ready to hand out my Mathematica code to anybody who wants it. I'll check for good ways to share it.
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My statistic professor says so, all the books that I look at state it:  is unscientific. You must derive a hypothesis from theory first, and then collect data and analyse it.  But I really don't understand what the problem is.  Suppose, I see sales figures for different car colors and form the hypothesis that from numbers of different-colored cars sold the largest group of cars on the street shoud be white. So I sit at some street one day and note all the colors of all the cars that pass me. Then I do some tests and find whatever.  Now, suppose I was bored and sat at some street one day and noted all the colors of all the cars that passed me. Since I love graphs, I plot a pretty histogram and find that white cars form the largest group. So I think that maybe most cars on the street are white and perform some tests.  How and why do the results or the interpretation of the results of the post-hoc test differ from those of the theory-driven* hypothesis test?  *&nbsp;What's the name for the opposite of a post-hoc test, anyway?    I would like to add that most of our knowledge about the universe (the Earth moves around the Sun) is deduced post hoc from observation.  It seems to me that in physics it is perfectly okay to assume that it is not coincidence that the sun has been rising in the East for the last thousand years.
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Electrons   have a much bigger charge density as the protons (and especially lead nuclei), aren't compound particles as the protons (and especially lead nuclei) are able to get a much bigger energy with the same fields as the protons (and especially the lead nuclei).   Why seems common for the big colliders after the LEP to use protons (and much bigger nuclei)?  Reacting comments: Yes, to get good experimental data about quark matter they need a lot of hot quarks (= collided big nuclei). But to create new particles, the energy per degree of freedom needs to be maximized, and this maximum is at the single particle with the highest charge density, and this is the electron.
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When we first discovered the proton and neutron, I'm sure scientists didn't think that it was made up of quark arrangements, but then we figured they could be and experiments proved that they were.  So, what is it about the electron that leads us to believe that it isn't a composite particle? What evidence do we have to suggest that it it isn't?
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My Young's slits experiment doesn’t work. I mean I tried to see wave effect of light but I didn’t see any thing expect particles! I’ve sent you a pic of my laser and a short video of the experiment. Is there any problem you think?
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Quantum mechanics allows us to describe a particle as a wave, and also a collection of particles, which a car happens to be. What separates a typical wave from a classical particle is that the position is not well defined for a wave.  I think that it is hard to tell exactly how big an atom is, because the electron of the atom may be anywhere, but the probability of finding the electron gets very small as you look far away from the nuclei. I think in some sense the atom is as large as we want, depending on the definition.  When a car drives past me, is the position of the car separate from my position in a quantum mechanical way, or is it correct to say that "part" of the car hit "part" of me? I understand that no matter the answer the force from the hit is so small that it is negligible in every way, but that is not the core of the question.  In addition, if I made any wrong claims, please correct me, thanks in advance.
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Hey,  trying to finish an assignment but having some trouble with it. I will show all my work. The topic is on wave/particle dualty, uncertainty principle (second year modern physics course).  So the question is:     Calculate the de Broglie wavelength of a 5.7 MeV α particle emitted from an atomic nucleus whose diameter is approximately $1.6 \times 10^{-14} m$.   So I know the de broglie wavelength is $\lambda = h / p$. But we dont know p in this case, however we do know the energy. So to relate energy and momentum I use the following formula:   $$ E^2 = p^2c^2+m^2c^4$$   using $m = 6.644 \times 10^{-27}$ and using $ E = 9.13\times 10^{-13}$ gives me a complex solution. (Check WolframAlpha)  Now I've tried leaving the energy in terms of eV and MeV and they give me real solutions however the answer is not correct.  The answer is 6.02 fentometers.  Anyone have any advice?
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When an alpha particle is emitted, two protons and two neutrons leave the nucleus but the electrons remain the same in number. Why does the atom remain uncharged although it appears it should have a net charge of $-2e$?
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I'm writing a piece about the electron, and I'm having trouble finding evidence to back up the claim that the evidence is pointlike.   People  the observation of a single electron in a Penning trap shows the upper limit of the particle's radius to be 10-22 meters. But when you look at Hans Demelt’s  you read about an extrapolation from the measured g value, which relies upon "a plausible relation given by Brodsky and Drell (1980) for the simplest composite theoretical model of the electron". This extroplation yields an electron radius of R ≈ 10-20 cm, but it isn't a measurement. Especially when "the electron forms a 1 μm long wave packet, 30 nm in diameter".    It's similar when you look at  by Brodsky and Drell. You can read things like this: "If the electron or muon is in fact a composite system, it is very different from the familiar picture of a bound state formed of elementary constituents since it must be simultaneously light in mass and small in spatial extension". The conclusion effectively says if an electron is composite it must be small. But there's no actual evidence for a pointlike electron.   Can anybody point me at some evidence that the electron is pointlike?
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From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this:   Solve the time-independent Schrodinger equation to find the energy eigenstates.  There will be a continuous spectrum of energy eigenvalues. In the region to the left of the potential, identify a piece of  the wavefunction that looks like $Ae^{i(kx - \omega t)}$ as the incoming wave. Ensure that to the right of the potential, there is not piece of the wavefunction that looks like $Be^{-i(kx + \omega t)}$, because we only want to have a wave coming in from the left. Identify a piece of the wavefunction to the left of the potential that looks like $R e^{-i(kx + \omega t)}$ as a reflected wave. Identify a piece of the wavefunction to the right of the potential that looks like $T e^{i(kx - \omega t)}$ as a transmitted wave. Show that $|R|^2 + |T|^2 = |A|^2$.  Interpret $\frac{|R|^2}{|A|^2}$ as the probability for reflection and $\frac{|T|^2}{|A|^2}$ as the probability for transmission.   This entire process doesn't seem to have anything to do with a real scattering event - where a real particle is scattered by a scattering potential - we do all our analysis on a stationary waves.  Why should such a naive procedure produce reasonable results for something like Rutherford's foil experiment, in which alpha particles are in motion as they collide with nuclei, and in which the wavefunction of the alpha particle is typically localized in a (moving) volume much smaller than the scattering region?
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If you take any large nucleus and add protons to it, the electrostatic repulsion between them will make the nucleus more unstable, because the electrostatic force between them is more repulsive at a greater distance than the strong force is attractive  So how come if you add more neutrons, which don't have a charge and so there is no electrostatic force, the nucleus still becomes more unstable?  Also why aren't there groups of neutrons bound together, so purely neutron nuclei (because they are neutral, I'm guessing they couldn't form atoms, because of the electrons needed for an atom)
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This question is a sequel of sorts to my  about .  In the paper, the authors performed molecular dynamics (MD) simulations of parallel-plate supercapacitors, in which liquid resides between the parallel-plate electrodes.  The system has a "slab" geometry, so the authors are only interested in variations of the liquid structure along the $z$ direction.  In my previous question, I asked about how particle number density is computed.  In this question, I would like to ask about how the electric potential is computed, given the charge density distribution.  Recall that in CGS (Gaussian) units, the Poisson equation is   $$\nabla^2 \Phi = -4\pi \rho$$  where $\Phi$ is the electric potential and $\rho$ is the charge density.  So the charge density $\rho$ is proportional to the Laplacian of the potential.  Now suppose I want to find the potential $\Phi(z)$ along $z$, by integrating the Poisson equation.  How can I do this?  In the paper, on page 254, the authors write down the average charge density $\bar{\rho}_{\alpha}(z)$ at $z$:  $$\bar{\rho}_{\alpha}(z) = A_0^{-1} \int_{-x_0}^{x_0} \int_{-y_0}^{y_0} dx^{\prime} \; dy^{\prime} \; \rho_{\alpha}(x^{\prime}, y^{\prime}, z)$$  where $\rho_{\alpha}(x, y, z)$ is the local charge density arising from the atomic charge distribution of ionic species $\alpha$, $\bar{\rho}_{\alpha}(z)$ is the average charge density at $z$ obtained by averaging $\rho_{\alpha}(x, y, z)$ over $x$ and $y$, and $\sum_{\alpha}$ denotes sum over ionic species.  The authors then integrate the Poisson equation to obtain $\Phi(z)$:  $$\Phi(z) = -4\pi \sum_{\alpha} \int_{-z_0}^z (z - z^{\prime}) \bar{\rho}_{\alpha}(z^{\prime}) \; dz^{\prime} \; \; \; \; \textbf{(eq. 2)}$$  My question is, how do I "integrate the Poisson equation" to obtain equation (2)?  How do I go from  $\nabla^2 \Phi = -4\pi \rho$ to equation (2)?  In paricular, where does the $(z - z^{\prime})$ factor come from?   Thanks for your time.
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The possibility of randomness in physics doesnt particularly bother me, but contemplating the possibility that quarks might be made up of something even smaller, just in general, leads me to think there are likely (or perhaps certainly?) thousands of particles and forces, perhaps layers and sub layers of forces, at play that we do not know about. So this got me thinking about quantum mechanics.    I'm no physicist, but I do find it interesting to learn and explore the fundamentals of physics, so I'm wondering: Could the randomness found in radioactive decay as described in quantum mechanics be the result of forces and / or particles too weak / small for us to know about yet resulting in the false appearance of randomness?  Or rather, can that be ruled out?
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Is there any thing composed of elementary particles in this world that is not 3 dimensional? I know that there is graphite which is singular atom thick. Is there anything in this world that has no depth? So I guess what I am asking is there an object that does not have volume
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"No theoretical proof of the Pauli's Exclusion Principle can be given as yet and for the present it must be regarded as something empirical added to and regulating the vector atom model."   I've found it in Atomic &amp; Nuclear Physics by N. Subrahmanyam &amp; Brij Lal.   My question is "What was the motivation behind Pauli's Exclusion Principle? Is that just an ad-hoc intuitive attempt of Pauli to explain the Zeeman effect or it was derived on the basis of mathematics? If mathematical then how? "