exchemist

In simple terms, the key to the momentum:position thing is wave/particle duality. The momentum of a QM entity is inversely proportional to its wavelength (de Broglie's relation), i.e. proportional to frequency, while the probability of detecting the entity at a position is determined by (the square of the) amplitude of the wave. If you have a QM entity represented by a pure sine wave, it has only one frequency component, so its momentum is determined precisely. But a sine wave extends throughout space. So you have no idea where it is. Conversely, if you have a superimposed series of waves of different frequencies, with phases aligned to interfere constructively at one location, then, because of the frequency differences, as you move away from that spot they will start to interfere destructively. So then you have a situation where all the amplitude is in one location - the position is well-defined - .............but you have no idea anymore what the momentum is, because it is composed of lots of different frequencies and hence momenta. This idea of adding waves of different frequencies to obtain various non-sinusoidal waveforms is familiar to radio and hi-fi engineers. It's not a QM idea. For instance the reason why you need good high frequency response, way above what you can hear, in an amplifier is to reproduce transients faithfully, because those require a complex mix of frequencies including very high frequency components. The special ingredient in QM is de Broglie's insight, associating momentum (p) with wavelength(λ) : λ=h/p . (h is Planck's constant).

No, that won't help you, because while you are told the acceleration you are not told the velocity. What do you know about this scenario? You know distance and acceleration and you want to calculate time. So the formula you need is the one that relates distance, acceleration and time. If you know two of them, and you do, you can find the third.

This question clearly prompts you to do the calculation. You need the appropriate formula involving acceleration. What is it?

You're wrong about that: https://www.researchgate.net/publication/230076355_The_Effect_of_Light_on_Textiles

I seem to recall the use of a capacitor in conjunction with a resistance, to suppress arcing in the switching of electric motors. But that I think is to lessen the inductive spike when the current is interrupted. In a circuit with a simple resistive load I'm not sure what would make a difference.

Have we failed? Lead water pipes are removed nowadays (unless safely passivated by hard water deposits, as in my house), lead is no longer in petrol, Hg in seafood is a recognised issue and in consequence is not generally a problem........ I think it's a mistake to tot up the various past practices that we now recognise to be risky and label them as "failures", when actually they are successes, in that we've learnt to stop them. But your question remains a valid one in principle, of course. Let's see what the biologists have to say.

I suppose it might, but why would anyone do that? Why breed or create selected individuals to be tolerant to heavy metal pollution, when one can use straight forward pollution controls to stop heavy metals entering the environment and thereby protect everyone - not to mention the rest of the biosphere on which humanity ultimately depends?

Indeed. However in science there is one ineradicable prejudice, if you care to call it that, which is a prejudice in favour of models that are built on, and testable by, observation of nature. If you come forward with a model which does not have those characteristics, it isn't science. It could be metaphysics, poetry, religion, fantasy or nonsense, but science it is not. Ether cranks and Tesla cranks are two a penny on the internet. You would well to disassociate yourself from such people if you want to be taken seriously. And energy is not "vibrations". Energy is a quantity, assigned to physical systems according to a rule e.g. force x distance, with dimensions ML²T². It is a property of systems. Vibrations are a behaviour of certain kinds of systems. A vibrating system is one of many kinds of system that has energy as one of its properties, but energy cannot be said to be vibration. That is why I stopped reading.

You mention ether, Tesla and vibrations in your first sentence. That’s a terrible start. I stopped reading at that point.

You need protection from whirling clouds of electrons:

That's a result, then!

OK that's what I got too. I suppose the problem is that question in (iii) is not very clearly expressed. I had to read it several times to work out what was going on. I assume what they want is the concentration of the solution from the breakfast cereal after making it up to 250ml. Since you take 10ml of this and add the same quantity of thiocyanate solution to it, that operation dilutes it by half, doesn't it? So I'd have thought to get the concentration of the solution, you just double the result from (ii), don't you? But it's a funny question, since I'd have thought the interesting thing to work out would be how much iron there is in the original breakfast cereal, which you can now work out, since you know from the concentration of this solution and its volume how much iron it contains, and you also know it comes from 100g of cereal. But maybe you will do that in class later or something. (Please check my logic though, as I may have misunderstood the question.)

I'm not sure why you would think that. What concentration of Fe3+ did you calculate in (ii), i.e. for the solution made up from the breakfast cereal?

You will need to paste the relevant section into a post. No one is going to open unknown files. Also, please give an idea of your thoughts on tackling it, so we can see where to help. We will not just give you the answer, as you don’t learn anything from that.

Ah yes, mixtures of states. That doesn't fit the idea of clean separate dimensions, indeed. Well I hope @geordief gets something out this at least. It seems to me important to stress that Hilbert space is an abstract mathematical concept and one should not think of these "dimensions" in the loose way that the word is often employed in sci-fi, denoting a series of alternative universes to ours or anything like that.

Nice explanation +1. Regarding @geordief's question about QM entities and dimensions, I suppose eigenstates being orthogonal means each state a QM entity can be in is in a different dimension, doesn't it?

No. Aromatic compounds in organic chemistry are those containing an unsaturated ring structure with certain, particularly stable, numbers of π-electrons (the aromaticity rule, known as Hückel's Rule, being 4n +2). The classic and simplest aromatic compound is benzene (n=1) and there is a huge family of compounds containing the benzene ring as part of their structure. There are many more complex aromatic structures, e.g naphthalene (mothballs; n=2). A lot of them have a not unpleasant smell, which is presumably how they got their name in the c.19th, but I don't know the precise origin of the term. Some rings are "heterocyclic", which means one or more members of the ring is an atom other than carbon. There are examples containing nitrogen, e.g. the 5 membered ring pyrrole and the 6 membered ring pyridine (both n=1). Ammonia however, NH3, is something quite different, a small inorganic molecule. It has a powerful choking smell that irritates the eyes and nose. Nobody would describe it as aromatic. In my experience the only human beings that smell of ammonia are babies with soiled nappies that have not been changed quickly enough, in which bacteria in the faeces break down urea from the urine and generate ammonia.

Neither. It's fictional.

I suppose a matt black surface would collect most, but would convert it all to fairly low temperature heat, which is not as useful as electricity.

I was going to make the same point. I suppose it is true that the 2s also has non-zero electron density at the nucleus, so capture could in principle take place from the 2s as well as from the 1s, though with lower probability since the 2s electrons spend more time further out. Undoubtedly.

Heisenberg? I think it was he that established the operator:observable formalism and the use of matrices. But the development of QM was very much a collective effort: more so than relativity.

I must admit I haven't seen anything like this organised for a complete periodic table. I should have thought it would be quite difficult, as each individual radioisotope has a different decay mode, so you might need several different chains for each element if there is more than one radioisotope.

Interesting. But surely the only example of a chemically produced ion with no electrons is H+, isn't it (even that is doubtful)? And the proton is stable. Your beryllium example does not reflect that, obviously. The change they measured in electron capture rate was 1% - and this process is highly exceptional, which is why it was newsworthy. For people like Paul, it seems to me the best answer remains that radioactivity is independent of the chemical environment of the atom. That is 99% true at least.

Sure. It's the job of Darwin's famous "natural selection" to weed out the useful mutations and ignore or discard those that are useless or actively harmful. (Nowadays we know the mechanisms are more complex than just that, but the basic principle remains valid.)

Yes in general there will be a small proportion of radioisotopes in everything. Life on Earth has evolved around this fact. Our cells have systems that repair DNA damage, to stop this wrecking the stability of cell replication. Nevertheless, DNA damage from radioactivity may be one of the driving forces behind evolution! You need mutations to come from somewhere, after all.