swansont

“all due respect” usually indicates disagreement. One of the components of the PEP is that you have identical particles, as I indicated. If they are unique they aren’t identical. If it’s on “another shell” then there is some difference in its state (whatever you mean by A or 1; we do have actual physics terminology we could use) e.g. an electron in n=2 and the s state, can be spin up, and also have an electron in n=3, s state that is spin up. Such as you’d find in Ar. “on the left” really has no meaning in this context.

If electrons were unique they wouldn’t end up in all these different states. It’s because they are identical that they need to be in different n, l or m states to satisfy the Pauli exclusion principle

What I said conveys pretty much the same information about hyperfine structure as the quote you provided, so yes. Why do you ask?

Some quantum particles, like electrons and protons, behave like little magnets, owing to having a charge and intrinsic angular momentum (spin). So a “spin up” electron will have a different energy than “spin down” in the presence of a magnetic field, which is provided by the nucleus. This energy splitting is the hyperfine splitting.

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What are these layers you are referring to?

Of course density has a physical meaning, since you would typically have a volume of the material. The question here was the probability at the origin as well as nearby. The volume element depends on the surface area of the shell, so it’s smaller close to the origin, and zero at the origin, and this artifact of the math has to be included when discussing the significance of the wave function’s value. The nucleus has a physical size, so sure. The electron interacts electromagnetically and the fact the the electron can be found there accounts for the large hyperfine splitting of the s state as opposed to the p states, where the wave function has a node, and so doesn’t have nearly as strong an interaction. In alkali atoms the hyperfine splitting of the ground state is hundreds of MHz to >1 GHz, while the excited p-state is significantly smaller

But if it’s zero, are you considering a volume? How much mass do you have in zero volume, regardless of the density?

If you’re going to posit a civilization that is on the cusp of being technologically capable of interstellar travel, it seems reasonable to assume they are capable of solving solvable problems like global warming and population, which are more political in nature (i.e. it’s about the will to solve the problem, not the means)

To the extent that “a sphere with zero volume” is meaningful, yes. But also that probability density lacks physical meaning if you ignore the volume you’re looking at.

There’s a mundane mathematical aspect to it. In a 1D system in cartesian coordinates, the square of the wave function gives us a probability. But going to 3D this is a density, so the probability is not just the square of the wave function. And we’ve moved to a spherical coordinate system. The volume element integral includes r^2dr, instead of the dx we had before. If you solved for a 1/x potential in cartesian coordinates, you’re going to get a wave function that looks something like xe^-x/a (for x>0), i.e. something that goes to zero at the origin

This also explains the relatively large hyperfine splitting of the S state. That’s the solution to the Schrödinger equation. This has to be multiplied by the volume element, which depends on r and is zero at r=0, to get the physically meaningful quantity.

It isn’t. You might have only been looking at the wave function itself. The probability multiplies this by r^2, making it go to zero at the origin. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydr.html

Yes, it’s a mathematical consequence, because the equation that describes the probability is math. Quantum mechanics can be hard to conceptualize, as some ideas are at odds with classical, everyday notions. Such as the electron having some particle behaviors and some wave behaviors, and the way probability shows up in the way things work. The hydrogen radial wave function drops off as e^-r/a (and probability is the square of that) so while there is a probability of finding the electron far from the nucleus it is vanishingly small.

A whistle-blower is one who reports wrongdoing to their chain of command or a designated point of contact outside the chain. There’s nothing traitorous about reporting suspected criminal behavior to the authorities.

Which would have been fine in a thread on alternative power, but not in science news, which need to focus on the linked article

Wut They shoved all the downside/problems to the latter part of the article. How does the reactor shut down? Can the decay heat keep the salt molten? How are they making electricity? As I recall, a huge problem in these reactors is primary-secondary leaks. How are they dealing with that? (it won’t be as bad as with liquid sodium, but I imagine it’s still an issue)

This is related to whistleblowing…how?

There's evidence that supports one. Not so much for the other. There's evidence that supports one of these. Not so much for the other.

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Right, because it's not like something like this has ever happened! <wink, wink>

Just to clarify, because this is a little unclear: fission is not the source of heat after shutdown. It's called "decay heat" and comes from the decay of the fission products. As I stated earlier, the thermal energy you have to deal with in fusion would be the couple of grams of fuel at whatever the plasma temperature is.

The link provided by the OP suggests it is, or at least can be. Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. ... For n = 1 million, Xn is roughly 0.9999, but for n = 10 billion Xn is roughly 0.53 and for n = 100 billion it is roughly 0.0017. As n approaches infinity, the probability Xn approaches zero; that is, by making n large enough, Xn can be made as small as is desired,[2][a] and the chance of typing banana approaches 100%. The same argument shows why at least one of infinitely many monkeys will produce a text as quickly as it would be produced by a perfectly accurate human typist copying it from the original.

The context of the OP's argument is often "evolution can't happen because randomness" and then showing the big numbers as the conclusion. This ignores the point that chemistry isn't random (as we've brought up a few times), and is falsified by the Miller-Urey experiment (and yes, while it's true that the conditions of that experiment are likely not those of early earth, it demolishes the notion that such probability calculations are relevant, because you would calculate a low probability of those amino acids being formed, and you would predict the formation of molecules that don't form.) One part of the rebuttal to the OP is that only the creationists are asserting that all aspects of evolution are random, and you should never cite a creationist as a credible source of information about evolution.

Yes, but there are only a few grams of fuel in it at any given time, limiting the thermal energy, and it cools as it expands. https://www.iter.org/sci/FusionFuels