exchemist

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.

Yes indeed they always are. Radioactivity is a function of the stability of atomic nuclei. These are not affected at all by the way atoms may be combined in chemical compounds. Chemical bonding is entirely due to the electrons in the atom, which lie far outside the nucleus. In fact, to give you an example, the basis of carbon 14 dating relies on this. Carbon 14 is formed in the atmosphere due to its constant bombardment by cosmic rays. The result is that a certain proportion of atmospheric carbon dioxide molecules will have a C14 atom in place of the usual C12 one. When a plant absorbs this in photosynthesis, the carbon 14 is incorporated into a sugar molecule, generally used to build the cellulose skeleton of the plant. So a living plant always has the same ratio of C14 to C12 as the atmosphere does. However, when this is a tree that is cut down and used to build, say, a boat, if we dig the boat up 5000 years later we can tell when the tree was cut down by the amount of C14 that is left, the rest having decayed away, because C14 stopped being incorporated at that point and, being radioactive, it declines from that point on, so the ratio of C14 to C12 changes.

Adam and Eve set the original precedent, I suppose. I can't see it's a big deal in Christianity. To be honest, the issue in practice is not disturbing other people or drawing attention to oneself. That's very much a matter of where you are and what the expectations are in that situation. For instance it is quite normal to wear very little on the beach, but if one were to dress like that on the London Underground*, it would be a big distraction. So if you are nudists, in a place set aside for that, the person who would draw attention to himself would the one dressed in a double-breasted suit. * However when my late wife worked in Rio de Janeiro, it was perfectly normal to see a guy in speedos on the bus, with a surfboard under his arm, next to all the people dressed for the office.

Too late, it’s Saturday. Sorry.

Here is the best reply I got on the other forum: "They are vortex generators. They generate tiny vortexes very close to the wing surfaces, thereby disrupting the laminar flow near the wing. One of their most important functions is to make the stall break more gradual. If one wing of the aircraft stalls suddenly while the other wing is generating lift, the aircraft will roll violently towards the stalled wing. Using ailerons to try to counter this will just make it worse since ailerons increase the (effective) angle of attack of the wings when deflected downward, and thereby deepen the stall. They also slightly reduce stall speed by ensuring laminar flow is NOT maintained. This is somewhat counterintuitive since laminar flow is a very efficient regime for an airfoil to work in. But in a laminar flow airfoil, again the stall break happens very suddenly. The turbulence created by the vortex generators ensures that any stall occurs gradually by disrupting the (primarily) laminar flow over the wing, and allows the wing to keep flying while partially stalled. They also increase drag and reduce cruise speed at a given power setting. They are still seen as worth the tradeoff because they increase maximum takeoff weight by providing more margin against violent stalls at low airspeed, and the slowest airspeed that an airplane can get off the ground is one of the primary determinants in both runway length needed and maximum safe takeoff weight for a given runway." So my guess is they may look like lights at night, due to being illuminated by the rotating beam of a fuselage navigation beacon, but in fact they are vortex generators.

I suppose you might get some help from Fick's Second Law of Diffusion for gases: https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion But I can't help thinking it is a bit artificial to assume two parallel, laminar flows down the pipe, which mix solely by diffusion from each into the other. I's have thought that introducing some turbulence would shorten the length of pipe needed considerably.

No. Move to Europe, where these silly antiquated measures are not used.😁 More seriously, I went to school in the UK during the transition to metric units and had to learn both at school. If you live in a benighted country with these ancient systems, you just have to learn them, I'm afraid. P.S. I never knew a "cup" was an actual measure. We had to learn gills, quarts and gallons. It seems there are 2 gills in a cup. So I've learnt something today.

Yes I agree. However it is normal in most western countries for illustrations in children's books to show a mixture of sexes and ethnicities, simply to make sure all the children see the book, and the subject, as being "for them". Especially perhaps with maths, as this has some baggage of -ve stereotyping, viz. a history of being seen as "nerdy", or "for boys" and so forth. So if that's all it is, then it's disgraceful that books are withdrawn for it.

He's banned.

The integral, with respect to t, of 1/t is: ln t +C, surely?

A winglet is to reduce wasted energy from wingtip vortices. That is a different thing.