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is there any requirement to measure whether the durations of 9 192 631 770 periods of different primary frequency standards and/or of the same primary frequency standard in different trials, had been and remained equal to each other, by (presumably) unambiguous means (such as the "ideal clocks" described in MTW §16.4) ? There's no explicit mentioning of ...


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The most common approach to model the sound radiation from a vibrating body is generaly the same as in all wave cases: continuity is the key. Let's say that a sphere is vibrating (changing it's volume periodically), then the acoustic velocity of the air particles just on the boundary with the body must be the same as the velocity of the sphere surface. It ...


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May I ask what you think of as sound? If sound is the vibration of air- or in general any material agent- then sound is the sensation you get from the changes in the pressure of the air, it's what reaches your ear and then produces some signals interpreted in your brain. Sound is the vibration, not something produced by the vibration. This vibration which ...


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Take your hand and move it. By moving your air, you moving the air. This is what a vibrating object does - it moves the air. Sound is just the movement of air (or a liquid or solid).


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what happened with the electrons in this process? After fission, the potential that bound the 92 electrons changes. The alpha has too much kinetic energy and cannot trap the two electrons it needs. It will pick up electrons at it comes to rest in the material or the air. The remaining, now Thorium, nucleus reorganizes and the electrons are bound in the ...


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The electrons stay with the daughter nucleus. A good way to see this is by imagining the decay. Imagine an atom. A helium nucleus shoots out. By the definition of a nucleus, it has no electrons. Therefore, the electrons must still be on the atom.


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Three oxygen atoms do form a molecule (look up "ozone").


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Chemical bonds occur because of the outer electron shell also known as a valence electron shell. Oxygen has six electrons and it's valence shell. An atom wants 8 electrons in its valence shell. They both decide to share two electrons. That way they both have full valence shells. NaCl works because Cl wants 1 more electron and Na wants to get 7 more. Mg needs ...


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Well, the simple point is Kinetic energy depends upon the mass and the square of velocity. Even if the mass of the object in this case molecule is relatively greater than that of the other molecule, as long as the velocity is greater enough to balance the average kinetic energy, it will be uniform. To put it simply K.E = 1/2*(m*v^2).


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Kinetic energy is related to both the mass and velocity of a particle through the equation $T= \frac{1}{2}mv^2$ where $T$ is the kinetic energy of the particle. So you are correct that the oxygen particles will likely move slower, because they are more massive, but as long as the product of the mass and the velocity squared of the oxygen particles (on ...


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is there any requirement to determine (and possibly correct for) the perturbation, or "shift", of any and all primary frequency standards, besides the described "shift due to ambient radiation"? Yes. These are called "systematic errors" and they are the order of business pretty much all day, every day, at the metrology labs that implement frequency ...


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You are essentially correct. If you start on the real line with the Schrödinger equation $$ \left(-\frac12 \frac{\partial^2}{\partial x^2} + V(x) \right ) \psi(x) = E\,\psi(x),$$ then at every point $x_0$ where $V(x)$ is analytic you are guaranteed that $\psi(x)$ will be analytic in a neighbourhood of that point. However, if $V(x)$ is not analytic then you ...


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In nuclear physics, an exited atom is exited due to its nuclei spins being aligned in a energetically not minimized constellation. This can happen due to external energy intake or as a part of a radioactive decay where the mother nucleus' spin constellation is carried over but then nearly instantaneous changes in its daugther nucleus. The freed energy of the ...


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The notation is that of one specific isotope (isotopes are nuclides with the same number of protons) of the chemical element Pu. 94 is the number of its protons, which is also the total charge, 240 is the total number of nucleons (protons and neutrons). In a neutral Pu atom there will always be 94 electrons to offset the charge of the protons in the nucleus. ...


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Either. It's context dependent. Chemists generally mean the whole atoms, nuclear physicists usually mean the nucleus, and people not in those categories could mean either. And there are exception to all those rules or thumb. And the distinctions is important when people start throwing masses around because the mass of an electron is almost on the same ...


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Your assessment of the transitions which can occur, and hence the photons which can be emitted, is correct. However, the colliding electron does not go to one of the energy levels in the atom (as Sebastian already correctly pointed out). What happens is that the colliding electron can deposit its energy in the bound electron, 'promoting' it from the ground ...


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In general, energy levels apply to the system1 (in your case the system of electron(s) and nucleus is the atom). So it is entirely appropriate to say that the atom is excited. It is only a few cases where it makes sense to factor the notion out and say that "this piece of the system" is excited. That works OK with hydrogen-like atoms because the nucleus is ...


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Now I assume that the question is asking the following: When an electron of energy 12.1eV collides with this atom, photons of three different energies could be emitted. Show on the diagram (with arrows) the transitions responsible for these three photons. Because from one single collision the emission of three photons doesn't make much sense to me. The ...


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Photons can be emitted when electrons change energy levels. You say that you have worked out where a 12.1 eV difference is. In an ordinary hydrogen atom, the electron will be in the $n_1$ state. Now, what energy state will the electron be in if an ordinary hydrogen atom absorbs 12.1 eV of energy? After absorbing that energy, the electron can lose energy ...


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As a matter of fact the list of the corrections to the hydrogen atom goes on and on. This is a list of corrections to the hydrogen atom and their order of magnitude for comparison. Bohr energy, which is very rough version of the hydrogen atom $\sim\alpha^2m_ec^2$ Spin orbit coupling (AKA Fine structure of hydrogen) $\sim \alpha^4m_ec^2$ Hyperfine splitting ...


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If you have a ground state hydrogen atom, the the first excitation energy is the distance to the lowest unoccupied orbital i.e. it is the lowest energy that can excite an electronic transition. The ground state is with the electron in the $1s$ orbital, and the next lowest energy orbital is the $2s$. So the first excitation energy corresponds to the ...


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Electrons occupy shells characterised by the principal quantum number, $n$. The lowest energy shell ($n=1$) is the ground-state. Above that you have the first excitation shell ($n=2$), the second excitation shell ($n=3$), and so on. In the hydrogen atom, the energy states are given by the equation $$ E_n=\frac{-13.6\,\mathrm{eV}}{n^2} $$ So the energy to ...


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Nuclei have a very small electric dipole moment. However, they can have a significant quadrupole moment, which influences hyperfine structure. You can refer to the Wikipedia article to get a quick understanding of the latter.


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Neither the nucleus nor the electrons form electric dipoles of any kind - the electron is a point charge, a monopole; the nucleus contains only one type of charge, the positive protons (and the electrically neutral neutrons). There is no scope for electric dipole interactions between the nucleus and electrons. The nucleus can still have an electric ...


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L I Komarov and T S Romanova 1985 J. Phys. B: At. Mol. Phys. 18 859 The algebraic method of solution of the Dirac equation for a particle in a Coulomb potential Abstract:An equation is constructed in two-dimensional complex space, in the set of solutions of which solutions of the Dirac equation for a particle in a Coulomb potential are present. These ...


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At the Large Hadron Collider we have studied matter down to a length scale of about $10^{-19}$ metres, which is about a billion times smaller than an atom. All the results so far confirm our existing theories. So it seems very unlikely that an undiscovered class of small atoms exists. The size of an atom depends on well understood physical principles. At ...


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I think your assumption that orthohydrogen and parahydrogen should have different bulk magnetic properties is dubious. Magnetic behavior is strongly dominated by electronic properties, because the Bohr magneton, $$ \mu_\text{Bohr} = \frac{e\hbar}{2m_\text{electron}} $$ is larger than the nuclear magneton $$ \mu_\text{nuclear} = ...


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I'm going to assume you are interested in regular old Nitrogen with configuration $(2p)^3$. In this case there are "6 choose 3" (i.e., twenty) different configurations consistent with the exclusion principle (you should be able to pretty easily write them all down pictorally). It's pretty easy to see that one of the configurations has $M_L=2$ and ...


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Angular momentum is that which is conserved under rotations. Equivalently, the angular momentum operators are the generators of rotations. This holds both classically and quantumly by (versions of) Noether's theorem. Defining "angular momentum" as $\vec x \times \vec p$ classically and then showing that it is conserved is doing it the wrong way around from ...



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