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what is the 1D solution for the particle in a box for fermions with spin?[edit]
All discussions of fermions in a box seem to involve 3D boxes. But what about 1D boxes? 71.207.151.227 (talk) 01:37, 7 October 2012 (UTC)[reply]
Thanks to uncertainty, you can't pin a good fermion down. Interesting applications have been made using Quantum wire however. Hcobb (talk) 02:08, 7 October 2012 (UTC)[reply]
Pardon me for being ignorant (BSc in something that probably isn't a science...), but is it possible to fit a fermion into a one-dimensional box? Don't they occupy a (small) volume of three-dimensional space? Or does 'box' mean something else entirely in this context? AndyTheGrump (talk) 04:53, 7 October 2012 (UTC)[reply]
AndyTheGrump: I think our Particle in a box page may help clarify. The use of a conceptual/mathematical solution in one dimension makes the math more tractable, with solutions generalizable to higher dimensions. -- Scray (talk) 17:14, 7 October 2012 (UTC)[reply]
It's analogous to the 3D problem. I think you are working directly in the limit of a large volume, otherwise there wouldn't have been a question about this. In that case, you need the density of states. In general, the number of single particle quantum states for a spin 1/s particle in some large volume V and in a volume of momentum space Vp is given as
2 V Vp/h^n, where n is the number of dimensions. The factor 2 is the spin degeneracy, i.e. it takes into account that for each wavefunction in configuration space, you have two independent spin states. Count Iblis (talk) 15:32, 7 October 2012 (UTC)[reply]
Will Santa Claus' house be underwater by 2020?[edit]
Will Santa Claus' house be underwater by 2020? And how will scientists explain this to all the children of the world? 220.239.37.244 (talk) 02:16, 7 October 2012 (UTC)[reply]
I suspect that most wise scientists avoid formal discussion and attempts at explanation of Santa's house. HiLo48 (talk) 02:58, 7 October 2012 (UTC)[reply]
Since Santa needed to get a 2nd mortgage to cover Rudolph's alcoholism treatments, his own Weight Watchers membership, and the cost of human growth hormone treatments for all his helpers afflicted by dwarfism, he was unprepared for the collapse in real estate prices. So, yes, his house is already underwater. StuRat (talk) 04:53, 7 October 2012 (UTC)[reply]
It's sad that with mortgages being in the news so much over the last few years, this really was the first definition of "underwater" that came to my mind. However, my thought concerning it was that the mortgage was probably paid off at least a hundred years ago. Eric (EWS23) 08:54, 13 October 2012 (UTC) [reply]
Bear in mind that the underwater period will be during the summer, when he and his fellow kallikantzaroi are working busily deep underground. Wnt (talk) 21:30, 7 October 2012 (UTC)[reply]
No, and, generally, warm-blooded animals can't, since it would be difficult to see beyond their own infrared glow, to see, say, the glow of a mouse in some underbrush. StuRat (talk) 06:08, 7 October 2012 (UTC)[reply]
You're welcome. I'll mark this Q resolved. StuRat (talk) 21:33, 7 October 2012 (UTC)[reply]
Well, resolved, but I'd add this, from our article cat senses: Cats are able to distinguish between blues and violets better than between colours near the red end of the spectrum. - Nunh-huh 22:56, 7 October 2012 (UTC)[reply]
I'm removing the resolved tag; such tags aren't recommended (the recent discussion on the Ref Desk talk page touches on the reasons why). Also, I notice that no one has provided a single source for their statements, which is very disappointing, given that this is a Reference Desk.
Moreover, StuRat's responses are inaccurate and imprecise, at best. There is published literature (some of it, which I've linked below, is both online and free of charge) which reports on the sensitivity of cat's eyes to near-infrared radiation.
Both studies note that the sensitivity of the cat's eye to far-red and infrared radiation is certainly lower than to middle-of-the-visible-spectrum light, but both also demonstrate measurable responses at longer wavelengths. Gekeler et al. go out to 826nm (laser line illumination) and 875nm (IR emitting diode). Speaking from my own personal experience as a mammalian scientist with normal color vision, human beings can certainly see bright sources with wavelengths out into the middle 800's.
Delving a bit further into the question, we can ask what happens at wavelengths that get a bit longer—what happens when you hit 950 or 1000nm (1 micrometer)? Then you start to get stuck by the physical properties of water. Infrared light at 1000nm and longer tends to be strongly absorbed by water, which – inconveniently – is a major component of the vitreous humour that fills the eyeball.
For comparison, that the blackbody emission of a human-body-temperature object peaks way up around 10 micrometers. That's deep, deep into wavelengths strongly absorbed by water (passage through 1 cm of water will absorb 99.9% of infrared light at this wavelength; the eye is essentially opaque to these rays). Forget being blinded by one's own infrared glow—at these wavelengths one is blinded by the opacity of one's own eye. TenOfAllTrades(talk) 02:29, 8 October 2012 (UTC)[reply]
I think it's further worth noting that, at least in snakes, sensation of IR is not done by the eyes, but by specialized "pit" organs. Also, in snakes, there is no specific reception of IR wavelengths. Rather, the pits are structured in a way that crudely focuses radiant heat onto nerve endings that are actually sensing temperature. Someguy1221 (talk) 02:57, 8 October 2012 (UTC)[reply]
It may also be worth pointing out, in regard to StuRat's answer, that infrared is quite a wide spectrum. If, for example, cats were able to see one-micron light, that would be well into the near infrared range by almost anyone's standards, but there would be hardly any glare at all from the cat itself. Presumably Stu was talking about much longer-wave infrared, say around ten microns. --Trovatore (talk) 05:15, 8 October 2012 (UTC)[reply]
My point was that IR detection at useful wavelengths (ones that would allow them to see warm-blooded predators and prey) would be difficult due to their own glow at those frequencies. IR at other frequencies doesn't appear to have any advantage to a cat over visible light. StuRat (talk) 21:12, 8 October 2012 (UTC)[reply]
Cat's and humans use the same proteins and mechanisms to see the longer wavelengths from the visible spectrum, just as most animals, so there will be little difference between them. The ability to capture more light will also help in seeing some near infrared, but I don't think they can see longer wavelengths than humans can (although humans may require higher intensity levels). There doesn't seem to be a protein or other biological mechanism that makes it possible to see much longer wavelengths than 850nm. Porphyropsin might add slightly to the range, but other than that, I don't know any.
In the UV range, there will be much more diversity, since the higher the frequency of the light is, the more chemical and biochemical mechanisms exist that can be influenced by it.
As Someguy1221 points out, the IR vision in snakes is based on temperature sensing, not direct IR vision. The pit organ's reflectivity in the visible spectrum is very high, had it not been, it would also detect visible light, and be useless to the snake I presume. Ssscienccce (talk) 21:12, 8 October 2012 (UTC)[reply]
I've tested my color-vision range with a spectroscope some time ago, and found out that I can see even faint IR sources at wavelengths of up to 800 nm at least (to me, they appear a dark reddish-brown). Does this mean that I'm a cat? ;-) 24.23.196.85 (talk) 02:31, 10 October 2012 (UTC)[reply]
It doesn't have a permanent dipole but its electron density map (why can't I find a basic electron density map of it online?) would be strongly polarised, with the carbonyl oxygens retaining most of the electron density and the carbonyl center being electropositive. Yet why doesn't carbon dioxide remove some of the slightly polar flavor compounds that are found in caffeine (CO2-water partition coefficient at least 0.3?) ? It has some polarity, right, just not dipolarity. 71.207.151.227 (talk) 16:35, 7 October 2012 (UTC)[reply]
This is a quadrupole. This is not what CO2 looks like. No, it has no polarity. A "quadrupole" would look like the pic I am appending. Think of it this way: the two diametrically oppose oxygens are pulling electrons equally from each other across the carbon atom. That creates a roughly equal distribution of electrons across the whole molecule. In general, any molecule which shows perfect VSEPR symmetry (i.e. one of the basic 3 VSEPR shapes: linear, trigonal planar, or tetrahedral) will be perfectly non-polar, so long as every point is the same atom, like CO2 where both atoms attached to the central atom are oxygen. This is true even where there is a large difference in electronegativity among the individual atoms, because those electronegativity differences will, in essence, counteract each other. So even molecules like tetrafluoromethane show the same nonpolar character as methane; CF4 and CH4 have comparable melting and boiling points because they are equally nonpolar, the difference is explainable by differences in London dispersion forces due to the difference in molecule size. --Jayron32 18:46, 7 October 2012 (UTC)[reply]
Apparently the quadrupole moment of carbon dioxide is -4.1 x 10-26 e.s.u.,[1] considerably stronger than that of nitrogen, hydrogen, and methane, which (hopefully) can permit its separation from exhaust by certain three-dimensional porous structures intended to mitigate greenhouse emissions.[2]Wnt (talk) 21:28, 7 October 2012 (UTC)[reply]
Well, there you go. --Jayron32 01:32, 8 October 2012 (UTC)[reply]
Is it wrong to say that we come from the monkey?[edit]
Actually, it's from the apes, but maybe the apes came from the monkey, so it's not wrong after all. OsmanRF34 (talk) 22:42, 7 October 2012 (UTC)[reply]
See [3]. We are on a parallel evolutionary path with monkeys, not direct descendents from them. Our common ancestors are all extinct. StuRat (talk) 22:59, 7 October 2012 (UTC)[reply]
Well, even if our common ancestors are extinct, they still could be called 'monkeys.' BTW, I am afraid the graphic you linked to is not the evolutionary perspective, but just the present day classification. OsmanRF34 (talk) 23:32, 7 October 2012 (UTC)[reply]
I would interpret StuRat's linked diagram to mean "yes". While it is true that the early ancestors of monkeys and apes, living at a different time than the present and not being a member of any modern clade, might be called whatever we wish, still, it seems logical to call the single common ancestor of "New World monkeys" (Platyrrhini) and "Old World monkeys" (Catarrhini) a "monkey". The catch there is that "monkey" is not a monophyletic group, since it includes a subgroup of "apes" that by tradition are not called monkeys, and if you're not defining it monophyletically, you can define it a lot of ways - for example, you could define it to include every one of the individual subgroups but not the common ancestor. But I think that's a stretch. Wnt (talk) 00:51, 8 October 2012 (UTC)[reply]
Biologists use precise terminology to avoid getting bogged down in semantic issues like this. A biologist would say that we are descended from animals that belong to the group simiiformes, which includes monkeys and their ancestors. Most biologists when speaking informally would probably apply the term "monkey" to everything in simiiformes, but there is no official rule governing this. Looie496 (talk) 00:50, 8 October 2012 (UTC)[reply]
Apes, including Humans, are Catarrhines. Our common ancestor with the Catarrhine monkeys would be itself considered a catarrhine monkey. Its common ancestor with the platyrrhine monkeys would also be considered a monkey. Yes, we are descended from some animals which, if they were living today, would unambiguously be considered monkeys. μηδείς (talk) 04:10, 8 October 2012 (UTC)[reply]
I am stuck on this physical chemistry question and would really appreciate some help. Here goes the question
Many processes such as the fabrication of integrated circuits are carried out in a vacuum chamber to avoid reaction of the material with oxygen in the atmosphere. It is difficult to routinely lower the pressure in a vacuum chamber below 1.0 * 10^-10 Torr
A) Calculate the molar density at this pressure at 299K
Well this is just simple substitution: P = ρ R T where ρ is the molar density
ρ = P/RT
= 1*10^-10/(299 * 62.36)
= 5.36 * 10^-15
B) What fraction of the gas phase molecules initially present for 1.0 atm in the chamber are present at 1.0 * 10^-10 Torr?
This is the tricky part. I know that PV = nRT and when you lower the pressure from 1.0 atm (760 torr) to 1.0 * 10^-10 torr, and assuming that V and T are held constant, n is lowered as well. Since molar density is defined to be the number of moles over volume
State 1 = 760 torr
ρ1 = n1/V = P1/RT = 0.0407
State 2 = 1.0 * 10^-10 torr
ρ2 = n2/V = 5.36 * 10^-15
The ratio of n1 to n2 can be calculated by dividing ρ1 by ρ2 which equates to 1.32 * 10^-13.
The online homework system is telling me that my answer is wrong and I am just trying to figure out what I did wrong. Any help is appreciated! Thanks in advance! — Preceding unsigned comment added by 169.232.236.95 (talk) 23:03, 7 October 2012 (UTC)[reply]
I worked it out without looking at your method, and got the same answer as you (1.322 x 10-13). Does the online system give you their numerical answer? If you can post that, we might be able to spot a mistake they made. Ratbone124.178.60.218 (talk) 00:25, 8 October 2012 (UTC)[reply]
Remembering a similar problem with a computer program checking answers some time ago, maybe you should try giving the answer as 10-10/760 or 10-11/76 instead of the rounded off result. Ssscienccce (talk) 21:32, 8 October 2012 (UTC)[reply]
I've never seen an automatic physics or chemistry homework checker that wanted a raw fraction when asking for something that can be solved as a numerical value. As far as rounding though, I have seen several that only accept an answer as "correct" if it is the proper number of significant figures (as well as numerically correct obviously). DMacks (talk) 21:46, 8 October 2012 (UTC)[reply]
It turns out that the program accepts the fraction 10^-10/760. I think it was a significant figure issue. Thank you all! — Preceding unsigned comment added by 169.232.236.127 (talk) 22:40, 8 October 2012 (UTC)[reply]
Credit to StuRat who taught me. @DMacks: Maybe the programs are getting better? I remember how much my teachers disapproved of rounded off results when the answer could be presented by a short, simple expression like a fraction or square root. Ssscienccce (talk) 08:24, 10 October 2012 (UTC)[reply]
They probably are. All secondary school students (in the UK) these days tend to have calculators which are capable of giving answers as fractions and even surds. You have to be more cunning about testing for true understanding, where you used to have the lazy option of simply requiring exact answers (when calculators would only give a decimal approximation). It causes me a moment of wonder, every so often, that they all carry these little things that display such answers.. 86.159.77.170 (talk) 19:47, 11 October 2012 (UTC)[reply]
I have not been very impressed with automatic checking programs so far. It seems as though they are doing a character comparison with a small list of allowed "correct" answers. So, if the answer is supposed to be exactly "0.48", you have to rely on the person who entered the allowed answers having entered both ".48" and "0.48". If not, one will be marked wrong. Then, when you add in the possibilities of answers like "48/100", "24/50", and "12/25", those would each have to be supplied to the program as correct answers, too, as would scientific and engineering notation. The result is that you can spend more time trying to guess what format(s) are allowed for the answer than actually doing the problem. StuRat (talk) 00:47, 14 October 2012 (UTC)[reply]
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