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9

Well, we could say, yes, that is simply how quantum mechanics works. But these are not the axioms of quantum mechanics, and the exclusion principle in particular is really only understood in the context of quantum field theory. The electron does not "spiral in" because it doesn't move in the classical sense at all. At the scale of the size of an atom, ...


6

The total angular momentum of a closed shell is zero because for fixed $l$, we have the possible states labeled by eigenvalues of $L_i$ as $m_{l,i} = l,\dots,0,\dots,-l$ in integer steps. The sum over all $m_l$ inside a shell is always zero, so total angular momentum of a shell is zero. This is just the generalization of the argument with "up/down" for ...


5

A typical atom is roughly a few times $10^{-10} \text{m}$ wide. A piece of paper is say $(1/4) \text{m}$ wide. Therefore the ratio of the width of an atom to the width of a piece of paper is around $10^9$. A piece of paper is roughly the same width as a human, so $10^9$ is also a rough guess for the ratio of the width of a human to the width of an atom. The ...


4

Technically, both solids and gasses have quantized energy levels. The difference is that molecules of a gas interact with other molecules very weakly, so the energy levels observed in emission or absorption of a collection of gas molecules are almost exactly the same as the energy levels that would be observed if you had a single gas molecule in isolation. ...


3

The typical way to handle such things is the "sudden approximation". The time scale of the decay/capture process is assumed to be much smaller than the time scale of the evolution of the electron shell. The probabilities of the new states will then just be the projections of the old state to the new stationary states. (The typical analytically solvable ...


3

For a 6 year old, you might want to focus on thickness instead of length, as the numbers get too big with length. A ream of paper (500 sheets) is a bit over an inch thick, say $3.5 \, \text{cm}$, so one sheet is $3.5/50 \, \text{mm}$, or $.07 \, \text{mm}$, which is $7 \times 10^{-5} \text{m}$. An atom has diameter $0.1 \, \text{nm}$ to $0.5 \, \text{nm}$ ...


2

Electron capture: $p+e^-\rightarrow n+\nu_e$ Beta plus decay: $p\rightarrow n+e^++\bar{\nu_e}$ Let's check the masses of both sides of the processes: Electron capture, initial state: $m_p+m_e=938.78 \frac{MeV}{c^2}$ Final state: $m_n=939.56 \frac{MeV}{c^2}$ The difference: (Final minus initial) $0.78 \frac{MeV}{c^2}$ Beta plus decay: (Positron emission) ...


2

In quantum mechanics the equation of motion is the Schrödinger equation $$ i\hbar\,\frac{\partial}{\partial t}\,|\psi\rangle = H|\psi\rangle $$ where the (self-adjoint) operator $H$, the Hamiltonian, determines its evolution. The energy levels are, by definition, the eigenvalues of such operator in its domain of definition $\mathcal{D}_H$. Spectral theory ...


2

Indeed, this is a very good question and far from obvious. From a classical point of view one can only argue using charge distribution and atom radius/ion radius. The more spherical the charge distribution in the atom, the lower its energy in an electric potential, because the more spherically it is, the more neutral the atom in respect to the potential. ...


2

Electron is a particle with mass and a certain probability of being found at a given distance around the nucleus of an atom at a certain time. It caries a negative charge which makes chemical reactions possible since chemical reactions are driven by the electrostatic forces between electrons and positively charged protons which reside in the nucleus of the ...


2

Experiments with trapped ions generally use fluorescence for detecting the ions. This means that they use a strongish pump to take the ion from its ground state to a dipole-allowed excited state and wait for the ion to decay by emitting a photon in a random direction, and then re-run the cycle over and over. This means that each ion essentially emits one ...


2

Quantization is an experimental fact that forced physicists to consider theories that could explain the data. This happened in the beginning of the twentieth century. 1) black body radiation could only be explained by assuming that the radiation came in quanta, i.e. not in a continuous spectrum.) 2) The photoelectric effect showed that light behaved as a ...


2

The quantization of energy levels appears both in quantum and classical mechanics, and it is not a consequence of the Schrödinger equation. It is a consequence of confinement. In fact, anytime that a wave equation (any quantum equation for the wavefunction, or a classical equation for a classical field, e.g., EM field) has periodic boundary conditions in ...


2

The accepted airglow answer might be technically true, but it does not answer the question! The existence of an additional and very faint source of green light in the atmosphere does not explain the absence of the green light in the sunset sky gradient. I wasn't satisfied with other answers either. The only satisfactory answer I could find is this one. ...


2

This would certainly result in a change in energy levels if the nucleus changes charge; in addition, you would expect a electron ejected as well to remain overall neutral (though there are some stable ions). The simplest quantum model that would give you an idea of the energy changes for an atom are described by so-called "Hydrogen-Like" atoms. The ...


1

Would a photon be released due to changes in the electron orbital energy in this case or would it be transparent or absorbed elsewhere in other state reconfiguration? If something causes a vacancy in an electron inner shell, there can be a photon emitted. Two processes related to nuclear decay in which this often happens are electron capture and ...


1

The obvious Google search finds various articles on the subject, including this one that has a graph of excitation lifetime against temperature: The lifetimes vary from about 600$\mu$s to about 3ms, so a 5 kHz signal (200$\mu$s) would indeed appear steady.


1

Why is not really important, how is. If you ask yourself why then the answers can be many, for example Why does gravity make two masses attract each other? The answer is because it does, what is really important is how and for that you have a first theory, Newton's Law of Gravitation, this theory is only true for relatively small masses (or masses with ...


1

Disclaimer: I do particle physics / cosmology, so this is definitely outside my field, apply grains of salt to this answer appropriately. I think Reference [29] (Lin et al, arxiv reference: 1008.4864) honestly does a better job of explaining what is going on (which makes sense, the impression I get is that 1008.4864 is a foundational paper in this ...


1

It is possible to measure wavelengths of light to many decimal places. When you see accurate determinations of atomic energy levels, they were done spectroscopically, looking at absorption or, more commonly, atomic fluorescence. Since $E=hc/\lambda$, one can accurately convert between wavelength and energy. When excited, atoms emit many wavelengths of ...


1

Soft x-ray optics typically uses grazing reflections on suitable mirror materials and gratings (e.g. Pt coated optics) or crystals and the detection can be done with scintillators using CCDs or PMTs. Commercially available instruments have approx. 0.2eV resolution (2000 lines) while research grade instruments can achieve much higher resolutions e.g. 30000 ...


1

Hmmm... I'll take a crack at it. An electron is a negatively charged subatomic particle that orbits the nucleus of an atom, which contains a positively charged subatomic particle called a proton and a neutral subatomic particle called a neutron.


1

Let's take these separately Are all electrons always in pairs except the final single one if odd number electrons are considered? For a ground state atom, then this depends on the sort of shell you're looking at. If you have an odd number of electrons, the simplest sort of ground state will look like this. In this case, if you have unpaired ...


1

If you were considering a theoretical system, at $T=0K$, you would be correct in assuming a Hydrogen atom has no $n=2$ electrons. However, at high temperatures (Or any finite temperature actually), there is a chance that the atom would be excited. (Meaning there are $n=2$, and there could be $n=3$, and so forth also) In fact, the Balmer series is very ...



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