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4

The entropy of a single atom does not make sense per se, unless you specify the preparation. The entropy of a single isolated atom, fixed at a point, is indeed not defined – the entropy is, after all, a property of an ensemble not of a system. The entropy of an ensemble of isolated atoms prepared at a specific energy, on the other hand, is well defined (this ...


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Does it go from one state to another via straight line or it makes smaller and smaller orbits till it reaches the next orbit The electron is an elementary particle and as such, at the level of atoms, it can only be mathematically modeled by a quantum mechanical probability distribution. These spatial probability distributions for the electron of the ...


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Which form of carbon do you talk about? Graphite is conductor. Coal is a semiconductor (van Krevelen 1993; Speight, 2013a and references cited ... The highest resistances are observed with coals having 80–92% carbon; they can be considered virtual insulators. Diamond is the allotrope of carbon in which the carbon atoms are ... Most diamonds ...


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You can define velocity as $v=\frac{\sqrt{\langle \hat{p}^2 \rangle}}{m_e} $. For ground state $v=Z\alpha$.


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As phrased, this question suggests suggests a very Bohr-like image of electrons. This answer is intended to nudge you in the direction of a quantum model, but is by no means complete. Honestly, there's no way to understand QM without delving deep into the math, and even then its difficult to make a math <-> reality correspondence. Firstly: quantum ...


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Yes you can do that; the space and spin parts just have to have opposite symmetry characteristics so that the total wavefunction is antisymmetric.


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Let's think about a system that has a two-fold degeneracy for some given energy level. That is, two states $ \psi_{a} $ and $ \psi_{b} $, both of which correspond to energy $ E_{0} $. An example would be a spin-1/2 particle with a Hamiltonian that is spin-independent. Now imagine that when we apply a perturbation, H', to the system, the degeneracy breaks ...


2

De-exictation is the process of transitioning from a high energy state to a lower energy state; the photon emitted has energy equal to the difference in the energy of the two states. If we're tacitly assuming that we started with a system in the ground (i.e. lowest energy) state, then something had to put the electron into the higher energy state before we ...


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As @EntropicallyDriven mentions, matter-wave interferometry can be used for inertial navigation. Better clocks (in terms of both performance and size / weight / power) would help with pulsar navigation.


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One possible application of AMO physics would be inertial guidance systems based on atomic interferometers--similar systems are currently being investigated for missile guidance and have shown much higher accuracy than other methods. Inertial navigation systems don't rely on a network of GPS satellites, which obviously wouldn't be present on Mars (yet!)


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The color of the photon is related to its frequency $f$, which can be related to the energy of the photon by the expression $E = hf$, where $h$ is Planck's constant. Thus the different colors of the emitted photons describes their different energies. The next step is to determine why specific elements emit certain colors. This has to do with the different ...


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By definition, Thomson scattering is the elastic scattering of light by a free charged particle. Atoms cannot be described as such, but the electrons in an atom may approximate to free electrons if their binding energy is much lower than the photon energy. This might be true for X-ray wavelengths, although if the photon energy gets too high then elastic ...


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This is one of the first examples of energy levels for electrons within the atom! If we take the Bohr model, which imagines that electrons circle the nucleus on set orbits Each of these orbits has a corresponding energy. The electrons are more stable at lower energy levels, and thus, prefer to be there. When you provide energy to the electrons (in the ...


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In short, you must consider the total elements of the system for conservation of momentum. In this case, nearly all of the momentum is exchanged between the electron and a photon that is absorbed or radiated away (the light). Momentum is conserved, and is largely balanced by this electron-photon interaction, although smaller amounts may be exchanged with ...


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Angular momentum is conserved only if there's no external forces, in this case the electron gains energy by light or by heat wich is kinetic energy. They are both external forces so the conservation of angular moment does not apply.


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You can only have an inelastic collision between two bodies if one or both of the bodies have some internal degrees of freedom that can absorb energy. For example if you have a rigid sphere then the only type of energy it can possess is kinetic energy. If we collide two rigid spheres then conservation of energy means the sum of the kinetic energies before ...


0

So I actually integrated this a while ago, I thought I should share the result. It turned out rather simple with the right substitution. By the way I'm talking about both potential and charge disrtibution as a Debye-like. Point charge is straight forward... First we put the center of the charge density on the z-axis as mentioned in my question. I get $$ ...


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There are several broadening mechanisms, and you have to know how they "add" together. Since a Voigt profile is the convolution of a Gaussian and Lorentzian profile, you rightly calculated both widths rather than just the overall width of the Voigt peak. For the Lorentzian portion, the width is the arithmetic sum of the individual widths: $ \Delta ...


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The spin orbit coupling can be derived from the nonrelativistic limit of the dirac equation and is given by $$ H_{\text{s-p}} = \frac{\varepsilon_0}{2m_e^2c^2}\mathbf{\hat{s}}\cdot\left(\mathbf{E}\times\mathbf{\hat{p}} \right) $$ $\mathbf{E}$ is the total electric field acting on an electron, which consist of a microscopic electric field ...


4

Is it possible to prove in 2016 that the universe is made up of more discrete units than say an atom or quark? Physics is not mathematics, it does not prove anything. It measures and observes and fits mathematical models to data. These models become validated as long as their predictions are fulfilled. A wrong prediction falsifies a model and ...


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The pre-factor is exactly the same thing, look up what $R_H$ is equal to. The (Z-1) term, is due to the inner electrons shielding part of the nuclear charge such as the electrons involved in the X-ray transitions only see a reduced electric field. It's explained in the link you provided.


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You can also use that the shift in the energy eigenvalue due to a perturbation to first order is the expectation value of the perturbation in the unperturbed state. If you multiply the kinetic energy term by $\lambda$ and the potential energy term by $\mu$, you have essentially the same Hamiltonian, so you can write down the ground state energy without much ...


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The reason is that also other orbitals are occupied. For example for benzene using the hückel-method you will find following molecular orbitals. The three lowest lying are occupied because of the 6 electrons. The pauli exclusion principle cannot be violated!


3

Assuming I understand you correctly the quantity you refer to is the second electron affinity i.e. the energy absorbed in the gas phase reaction: $$ X^- + e \rightarrow X^{2-} $$ (it's the energy absorbed because a negative second electron affinity means energy is released) If so, there are no elements for which the second electron affinity is negative. ...


3

This is closely related to the questions: Why do non-hydrogen atomic orbitals have the same degeneracy structure as hydrogen orbitals? Which electron is first ionized $n=2,\ell=1, m=?$ Strictly speaking polyelectronic atoms do not have atomic orbitals because atomic orbitals exist only for a central force. In polyelectronic atoms the repulsion between ...


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Interaction between neutral atoms/molecules is described by such a potential that the force is that of repulsion at smaller distances and that of attraction at greater distances. The repulsion is Pauli repulsion, so it is (parts of) electronic orbitals that are between atoms/molecules. With higher temperature, the oscillatory energy is higher, and the atoms ...


2

The diffraction pattern is due to elastic scattering from the "ion core", which is the stationary net charge of the atomic nucleus and it's bound electrons; these elastically scattered electrons don't lose any energy. The electrons which interact with the free electrons are inelastically scattered, and contribute a foggy background to the diffraction ...


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What the scenario here is that you are comparing the photoelectric effect with X-ray diffraction. See a wave is a carrier of energy. IT could transmit energy from one point to another. But it cannot impart it's energy to another particle as a wave, but only by quanta of energy. That's what photoelectric effect tells us. An electron will be excited only if a ...



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