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25

The Sommerfeld model, and the Bohr model from which it is derived, are toy models developed in an attempt to describe spectral lines in the era before modern quantum mechanics. You might be interested to look at the question Is it possible to recover the old Bohr-Sommerfeld model from the QM description of the atom by turning off some parameters? for more on ...


19

Note well: What we perceive as color is bit of a tricky subject. This is a different question, one that has been asked and answered multiple times at this site. Per the typical human eye response, sunlight at the top of the atmosphere is about as "white" as "white" can be. Some of that incoming sunlight is reflected back into space, some is absorbed by the ...


18

The sky does not skip over the green range of frequencies. The sky is green. Remove the scattered light from the Sun and the Moon and even the starlight, if you so wish, and you'll be left with something called airglow (check out the link, it's awesome, great pics, and nice explanation). Because the link does such a good job explaining airglow, I'll skip ...


13

Further to John Rennie's answer, which I wholeheartedly agree with (insofar that the planetary orbit picture is outdated by nearly a century), you might like find the following interesting. If the electron really were like a planetary orbit, then it would generally be an ellipse rather than a circle. The force field has the same functional form as the ...


11

You are missing nothing. The Bohr model of the atom is false, and nowadays we replace the idea of the semi-classical "orbit" of Bohr with the fully quantum mechanical notion of orbitals or electron clouds, which give a probability distribution for the position of the electron around the nucleus, but do emphatically not imply that the electron is moving in ...


11

It is a very interesting question that allows to point out the differences between a Neutron Star and Nuclei. Although the dedicated article in Wikipedia Neutron Star fully covers the information, it is relevant to summarize here the elements. Nuclei are essentially different to Neutron Stars and some reasons are: Different bounding force: while Nuclei ...


8

The hand waving explanation in your question is called Rayleigh scattering Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle therefore becomes a small radiating dipole whose radiation ...


7

The nuclei of heavy elements (lead, gold, ...) approach the asymptotic density of extended nuclear matter (and therefore the density of neutron stars). The lighter elements do not. That said, it would be an error to refer to nuclei as "miniature neutron stars" because the binding force and dynamics are different. Nor are nuclei protected, shielded or held ...


7

The following passage has been extracted from Bohr's Nobel lecture: While in contradiction to the classical electromagnetic theory no radiation takes place from the atom in the stationary states themselves, a process of transition between stationary states can be accompanied by the emission of electromagnetic radiation, which will have the same ...


5

Why do electrons in an atom occupy only the stationary states? This isn't true. An electron in an atom can be in any superposition of states. This is one of the basic postulates of quantum mechanics: linearity. For example, say an atom has a ground state 1 and an excited state 2, and let's say we're able to prepare it in a pure state 2. It will decay ...


5

Firstly the Bohr model involves fixed orbits, not probablity distributions. Also, the Bohr model does not consider sublevels (such as 2s versus 2p). The concept of probabilty distribution is an interpretation of the Schrodinger equation wavefunction solutions. The 1s orbital has zero nodes, 2s has one node, 3s two nodes, etc. The 2p subshell has a ...


5

The sun is technically green because the peak of its black body spectrum is near green wavelengths. When light scatters parallel to the plane of incidence (i.e., during the day time), it is blue-shifted. When light scatters perpendicular to the plane of incidence (i.e., sunset or sunrise), it is red-shifted. The light that is not scattered but makes it ...


4

The probability density of the ground state is time independent, so there is no motion in this sense. Yet the expectation value of the kinetic energy is non-zero, so there is movement in this sense. How are these notions of movement reconciled? First off, classically, if we had a particle in a $1/r$ potential and released it from rest, it would indeed bob ...


4

I would guess the book is using the virial theorem, which states that for a stable system: $$ 2T = -V $$ This immediately gives us $T = kZe^2/2r$ and therefore the total energy is $T + V = -kZe^2/2r$.


3

From Maxwells equations we know that accelerated charged particles emit em waves. This can be seen from the electromagnetic wave equation, where a second derivative of the electric field is involved. If the second time derivative of the charge density is nonzero, also the second time derivative of the electric field is non vanishing and electromagnetic ...


3

That depends on what is meant by "solving" the atom. What Feynman probably is referring to is the usual atomic Hamiltonian, which is already an approximation from the field theoretic point of view (no strong forces, etc.). The main problem is electron-electron-interactions. If you have an atom with more than one electron, the interaction term between the ...


3

Almost but not quite. Qualitatively the spectrum is the same with the $1/n^2$ spacing, but the scale of the spectrum is set by the reduced mass $\mu$, $$\mu = \frac{1}{\frac{1}{m_l}+ \frac{1}{m_p}}$$ where $m_p$ is the proton mass and $m_l$ is the lepton (muon or electron) mass. Since $m_p \approx 2000 m_e$, it is not a large error to take $\mu = m_e$ for an ...


3

I think your confusion is cleared up quite simply: you're confusing the terms "orbital" and "electron shell". An orbital is characterized by the three quantum numbers $n,\ell,m_\ell$. This terminology makes sense, because these three numbers together completely determine the spatial component of the wave function. However, this leaves a freedom in the spin ...


2

Rather than write something unintelligible, I'll quote from a page on cesium clocks. According to quantum theory, atoms can only exist in certain discrete ("quantized") energy states depending on what orbits about their nuclei are occupied by their electrons. Different transitions are possible; those in question refer to a change in the electron and ...


2

The potential energy function is the same for both. The energy level solutions are the same for both. The key difference is that in (most modern interpretations of) the Schrodinger model the electron of a one-electron atom, rather than traveling in fixed orbits about the nucleus, has a probablity distribution permitting the electron to be at almost all ...


2

Various physical properties of materials including shear strength are connected to the strength of attractive forces between molecules -inter-molecular forces. The type of inter-molecular force determines the force and energy by which the molecules stick to one another. Inter-molecular force types include ionic bonds, hydrogen bonds, dipole forces and ...


2

Hopping and tunneling are often used as synonyms, but they are really very different terms with a fundamentally different basis. Tunneling is an inherently quantum-mechanical feature which means that a particle wave-function tends to overlap into it's energetically disallowed area which leads to a non-zero probability of finding it "where it should not be". ...


2

One reason we focus on energy eigenstates is that atoms spend almost all of their time in an energy eigenstate, and their spectrum is a result of transitions between them. Another reason is pedagogical: to peel back the onion one layer at a time. But before too long, many courses do include examples of systems that are not in an energy eigenstate. One ...


2

If you assume separability of the wave function, i.e., $\psi(\mathbf x)=u(x)v(y)w(z)$, you can solve the individual components separately: \begin{align} -\frac{\hbar^2}{2\mu}\frac{d^2u(x)}{dx^2}+V_1(x)u(x)&=E_1u(x)\\ -\frac{\hbar^2}{2\mu}\frac{d^2v(y)}{dy^2}+V_2(y)v(y)&=E_2v(y)\tag{1}\\ ...


2

Technically the electron and proton are both orbiting the barycenter of the system, both in classical and quantum mechanics, just as in gravitational systems. You find the same dynamics for the system if you assume the proton and electron are moving independently about the barycenter, or if you convert to a one-body problem of a single "particle" with the ...


1

The short answer is: protons are much more (1800 times) massive than electrons. That makes them (approximately) the center of mass of the system, that's why electrons are the ones orbiting protons and not vice versa. The term 'orbiting', however, means something essentially quantum. It is the reason of the stability of the atom (electrons don't radiate ...


1

You ask "How can an electron change orbitals staying at same positions, if it can then it must be able to do it all the time, why not only at the time of deexcitation?" Why do you think the electron needs to change position to jump from one orbital to another? Orbitals are energy states of an electron not "position" states. An electron simply needs to ...


1

I will stress what the other answers also include. The Bohr model does not have orbitals, but orbits, similar to the planet orbits around the sun. It is the first successful effort to describe the experimental behavior, i.e. the photon spectra, that excited atoms emitted. It postulated steady orbits. A postulate is like an axiom in a theoretical model that ...


1

One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would collapse with the nucleus. This is a common error in physicist's history of physics. The problem was not with Bohr's model, but (as Bohr thought) with ...


1

Interesting question. I would have thought that if you were aware of the exact number of energy states and the populations thereof, you could apply boltzmann statistics to each of the levels in order to fit an appropriate temperature to the population in each state. This temperature, if comparable amongst the included levels, would therefore require that the ...



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