Wikipedia:Reference desk/Archives/Science/2016 December 14

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December 14

Nitrogen gas VSEPR sketch

I've been unable to find a satisfactory answer to this: What would the central atom on N₂ be to draw an accurate VSEPR sketch? We were instructed to remove the electrons that appear in the Lewis structure from the non-central atoms, but keep those on the central atom... so would you remove both non-bonding pairs to make a sketch that looks like N:::N or keep them both, like :-N:::N-:? I presume that the orbitals hybridize, which I feel would mean keeping the non-bonding pairs, but I'm not entirely sure.

Thank you for any help you can provide, and sorry if this counts as asking you to do homework. — Preceding unsigned comment added by 71.30.39.180 (talk) 00:39, 14 December 2016 (UTC)

@71.30.39.180: Either atom works. Do not overthink this. The nitrogen atoms bond with a triple bond consisting of two pi bonds and one sigma bond. What hybridization delivers this? What does that look like? Remember to also obey the octet rule.--Jasper Deng (talk) 01:05, 14 December 2016 (UTC)

Indeed. The concept of a "central atom" is merely used to choose one atom around which to identify the hybridization, or to act as a vertex when measuring bond angles. The concept of a "central atom" only works well when dealing with "binary" molecules with a clear central atom, and the curriculum of your first chemistry class is highly constricted to presenting molecules like this (think CH₄ or NH₃) for purely pedagogical reasons: you first need to draw simple Lewis diagrams and identify bonding angles and hybridizations of simple molecules. Once you've learned VSEPR, you can apply the concepts to more complex molecules for which the idea of "central atom" is meaningless; what is the "central atom" of Isoleucine for example? Who cares; you can still use VSEPR to define rough bonding angles and hybridizations for every atom in that molecule. The same with N₂. Count the electron domains around either nitrogen atoms. Since it is exactly two in either case (the triple bond and the lone pair each are a domain), then the hybridization is "sp" and the angle between the domains (that is, the angle between lone pair and the triple bond) is 180 degrees. This analysis works for any molecule, no matter how simple or complex: Pick an atom, count the domains, and then you know the hybridization and approximate angles, since it is basically a one-to-one correspondence between all three. --Jayron32 04:19, 14 December 2016 (UTC)

Sigh... is it just me or is that first figure in Lewis structure completely fouled up? They give an instruction to "draw the least electronegative atom in the center with the other atoms spaced evenly around it" as if that were a law of nature and there's no such thing as peroxynitrite. More accurate instruction would be "look up the structure of nitrate", I think. And it would might make more sense to give the electrons first to the more electronegative elements, certainly not by position, though honestly again I think the answer is "look up the structure" because there must be good counterexamples even if I'm drawing a blank the past minute. Wnt (talk) 16:21, 14 December 2016 (UTC)

As noted, this is a pedagogy concern and not a "how real trained chemists would do this" concern. When someone is first learning, like the first day they have ever seen it in their life, nitrate is a fine structure to use as an example, and no chemistry teacher who as any good at their job at all would even bring up peroxynitrite in such a situation. When you hear hooves, you don't think "unicorn!" and when you see NO₃^- you don't think "peroxynitrite!". The rules for writing lewis diagrams as written are fine for non-chemists, and it's only helpful to bring up the weird stuff AFTER they've learned the basics. How one constructs a learning environment, including WHAT one teaches and WHEN one teaches it are VERY important to helping people learn, we can't just vomit random information and expect learners to just pick it all up on their own. Start simple with easy to follow rules, then once learners have learned the rules, introduce more complex issues. --Jayron32 16:36, 14 December 2016 (UTC)

Interpretation of size: "152 x 200 x 20 + 39 cm" of bed sheet

I saw on Ebay dimensions of bed sheet: "152 x 200 x 20 + 39 cm". What does this "+39 cm" mean? (what are these 39cm?) I saw it not only in store of one seller but in a lot of stores on ebay. I understand that the 152cm is the width while 200cm is for the length, then the 20cm is not clear as well as the "=39cm" for what they stand. 93.126.88.30 (talk) 04:10, 14 December 2016 (UTC)

Can you link to an example? --Jayron32 04:12, 14 December 2016 (UTC)

Yes I can. Look at the bottom of this page for example. 93.126.88.30 (talk) 04:15, 14 December 2016 (UTC)

Maybe 20 cm for the fitted part and then 39 cm for the pleated valence extension? DMacks (talk) 04:18, 14 December 2016 (UTC)

Yes, this shows up specifically on fitted valence sheets. Another form of the above dimension would be given as "152x200x20+39cm frill". So it's length X width X depth + frill-length. Someguy1221 (talk) 04:21, 14 December 2016 (UTC)

Too bad. I was looking for a nice Christmas gift for my 4-dimensional friends, and this sounded perfect. :-) StuRat (talk) 15:24, 14 December 2016 (UTC)

Considering that 39 cm is only equal to about 1.3 nanoseconds, wouldn't your 4-dimensional friends prefer something more durable? --76.71.5.45 (talk) 20:50, 14 December 2016 (UTC)

Must be a 4th spatial dimension, not a 4th temporal dimension. So they'd live in a 4+1D spacetime. Double sharp (talk) 07:32, 15 December 2016 (UTC)

Feynman Lectures. Lecture 41. Ch. 41–3 Equipartition and the quantum oscillator [1]

...

And now, how many oscillators are there? Of course, $N_{0}$ is the number that are in the ground state, $N_{1}$ in the first state, and so on, and we add them together: $N_{\text{tot}}=N_{0}(1+x+x^{2}+x^{3}+\dotsb )$. Thus the average energy is ${E}={\frac {E_{\text{tot}}}{N_{\text{tot}}}}={\frac {N_{0}\hbar \omega (0+x+2x^{2}+3x^{3}+\dotsb )}{N_{0}(1+x+x^{2}+x^{3}+\dotsb )}}.$ Now the two sums which appear here we shall leave for the reader to play with and have some fun with.

— Feynman • Leighton • Sands, The Feynman Lectures on Physics, Volume I

Can you show derivation?

I write next:

${\tfrac {0+x+2x^{2}+3x^{3}+\dotsb }{1+x+x^{2}+x^{3}+\dotsb }}={\tfrac {(x+x^{2}+x^{3}+...+x^{n})+(x^{2}+x^{3}+...+x^{n})+...+(x^{n})}{1+x+x^{2}+x^{3}+...}}=$
$={\tfrac {(x+x^{2}+x^{3}+...+x^{n})+x(x+x^{2}+...+x^{n-1})+...+(x^{n})}{1+x+x^{2}+x^{3}+...}}=$
Using formula for sum of geometric progression $Sum=b_{1}{\tfrac {q^{n}-1}{q-1}}$ we have:
$={\tfrac {x{\tfrac {x^{n}-1}{x-1}}+x^{2}{\tfrac {x^{n-1}-1}{x-1}}+...+x^{n}}{1{\tfrac {x^{n+1}-1}{x-1}}}}={\tfrac {x(x^{n}-1)+x^{2}(x^{n-1}-1)+\dotsb +x^{n}(x-1)}{x^{n+1}-1}}$
Opening parentheses:
$={\tfrac {x^{n+1}-x+x^{n+1}-x^{2}+...+x^{n+1}-x^{n}}{x^{n+1}-1}}={\tfrac {nx^{n+1}-(x+x^{2}+...+x^{n})}{x^{n+1}-1}}={\tfrac {nx^{n+1}-x{\tfrac {x^{n}-1}{x-1}}}{x^{n+1}-1}}.$

I can't simplify deeper. Feynman writes that the sums must give ${\tfrac {1}{x^{-1}-1}}$. I have checked that with $x=2;n=4$ and got $98/31$ and Feynman's formula gave $-2$ - the wrong answer. Username160611000000 (talk) 08:59, 14 December 2016 (UTC)

If the series converges (i.e. if $|x|<1$) then

$1+x+x^{2}+x^{3}+\dotsb ={\frac {1}{1-x}}$

and

$x+2x^{2}+3x^{3}+\dotsb =x{\frac {\operatorname {d} }{\operatorname {d} \!x}}(1+x+x^{2}+x^{3}+\dotsb )={\frac {x}{(1-x)^{2}}}$

so

${\frac {x+2x^{2}+3x^{3}+\dotsb }{1+x+x^{2}+x^{3}+\dotsb }}={\frac {x(1-x)}{(1-x)^{2}}}={\frac {x}{1-x}}={\frac {1}{x^{-1}-1}}$

You can verify this numerically if you try a value of x between -1 and 1. Gandalf61 (talk) 09:52, 14 December 2016 (UTC)

Thank you very much. Now I see that $\lim _{n\to \infty }{\tfrac {nx^{n+1}-x{\tfrac {x^{n}-1}{x-1}}}{x^{n+1}-1}}={\tfrac {0-x{\tfrac {0-1}{x-1}}}{0-1}}={\tfrac {x}{1-x}}$. But if n is number of energy states is it correct that n=∞?Username160611000000 (talk) 17:53, 14 December 2016 (UTC)

An infinite number of oscillators is not a physically realisable situation, but it can be a useful approximation for a large but finite number of oscillators. Feynman's analysis of the problem starts with the phrase "Suppose now that we have a lot of oscillators ...". This suggests he is interested in the asymptotic behavior of the average energy as the wavelength becomes very small and the number of oscillators becomes very large. Gandalf61 (talk) 09:25, 15 December 2016 (UTC)

Main Battle Tanks

Hello , how much difference is that between M1A2 and Leopard 2 in the issue of (MTBF) mean time between failures ?86.108.114.204 (talk) 14:17, 14 December 2016 (UTC)

Note that, from our mean time between failures article: "For complex, repairable systems, failures are considered to be those out of design conditions which place the system out of service and into a state for repair. Failures which occur that can be left or maintained in an unrepaired condition, and do not place the system out of service, are not considered failures under this definition." So a tank with more redundancy might remain operational despite the components being more prone to failure. StuRat (talk) 15:43, 14 December 2016 (UTC)

This [2] document from the Institute for Defense Analysis defines MTBF both for parts and for the system as a whole, and says, with reference "The M1A2 Abrams main battle tank has an MTBF of 27 hours", emphasis mine. SemanticMantis (talk) 17:13, 14 December 2016 (UTC)

So are you saying they have to fix them every day?! (emphasis mine) 2601:646:8E01:7E0B:F88D:DE34:7772:8E5B (talk) 13:31, 15 December 2016 (UTC)

I assume that means 27 hours of usage, not if it's just sitting there. 27 hours of continuous use would be unusual for a tank, as it would be for an ordinary car. So, if they do maintenance after each use, that might be enough. StuRat (talk) 16:11, 15 December 2016 (UTC)

27 Hours MTBF for the M1A2 Abrams is cited from a review in 2003. The implication is that a fleet of the tanks in uninterrupted operation for 27 hours will expect 50% of vehicles to show any component failure, likely including survivable defects such as air conditioner or radio failures. Experience from the Battle of Norfolk tank engagement was that friendly fire could be at least as lethal. The last day 28 February 1991 of that battle gives data on Abrams tank performance. The US 3rd Armored Division deploying some of their 360 Abrams tanks had 3 M1A1 Abrams tanks damaged during 24 hours of combat during which they destroyed or captured 547 enemy vehicles, including 102 tanks. Blooteuth (talk) 17:22, 15 December 2016 (UTC)

• You will have to specify the user as well, as different maintenance practices are going to be a significant contributor to the MTSF. In other words, there probably isn't a single answer. Fgf10 (talk) 17:38, 14 December 2016 (UTC)

Not really, overall availability is dependent on maintenance practice, but that's because mean time to repair (MTTR) is largely dependent on the maintainers, not the equipment. MTBF does not include the MTTR element, both must be calculated before an overall availability can be determined. Likewise, preventative maintenance can also improve availability. To take a simple example, if a switch with a specified lifetime of 10⁶ operations is replaced by routine maintenance at 10⁵ operations, that might result in less downtime than waiting for it to fail and having to send the equipment for repair (it can sometimes work the other way as well, at times in my past career I have had some routine maintenance tasks struck off the schedule because they were actually making things worse). None of that has any effect on the MTBF quoted by a manufacturer - that is down to the equipment alone. SpinningSpark 23:10, 18 December 2016 (UTC)

Does the cold itself cause to illness or the viruses are those which cause it?

Normally our parents used to warn us that "if you will not dress properly then we will catch cold". Then my question is if it's the cold itself which make the person ill or it's about viruses and then the question is what and why it matters if we were 2 or 4 layers while all those viruses enter through the respiratory system that is opened as usual without any special border/s or covers for the winter? (Attention please, I'm not talking about the reducing of temperature because in order to get what so called hypothermia ( a low body temperature) we have to to be exposed for the cold for a long time or to very low temperature in very cold places, and obviously I'm nt talking about that but normal cases which the body can hold its normal temperature) 93.126.88.30 (talk) 23:23, 14 December 2016 (UTC)

It's a virus, but cold weather sometimes can figure into it. See Common cold. ←Baseball Bugs ^{What's up, Doc?} carrots→ 23:27, 14 December 2016 (UTC)

It is the virus that makes you sick, but it is also possible that cold weather conditions could increase the chance of viral infection upon exposure. You could have a depressed immune response, or the cold/dry conditions could make body entry vectors easier for the virus, etc. --OuroborosCobra (talk) 03:26, 15 December 2016 (UTC)

Some factors I've heard of involve low humidity, which may allow the virus to survive longer on surfaces, and might make dry nasal passages more vulnerable to infection, and cold possibly reducing the chance of asymptomatic infection, and then of course there are gatherings like Thanksgiving and Christmas, which encourage people to share food extensively at the height of cold and flu season. There are many ways to catch cold - I think of contacting a surface and touching an eye or other mucous membrane as the worst, but I don't really know that; it's hard to quantify "overall". But one way you definitely do NOT catch a cold is through ordinary skin. The layers do not in any way prevent a virus from entering the body. Wnt (talk) 12:31, 15 December 2016 (UTC)

Also, moving between cold and hot environments causes the nose to run, and this, combined with poor hygiene practices, can result in snot on surfaces that spreads infection. StuRat (talk) 16:08, 15 December 2016 (UTC)

Cold weather plays a part because "rhinoviruses, which are the most common cause for colds, are better able to reproduce at temperatures just below the body’s 98.6 degrees Fahrenheit" but it's your nasal cavities that need to be kept warm [3]. Richerman (talk) 17:35, 15 December 2016 (UTC)

• Correlation is not causality. Viruses propagate better in crowded conditions, and humans crowd together more in the winter. 'Flu and "the cold" are therefore more common in winter, and Momma therefore learned from Granny that cold temperature causes sickness. -Arch dude (talk) 04:08, 16 December 2016 (UTC)
  • What cold air does to the nasal passages can contribute to vulnerability to the virus. But you can get a cold any time of year. There used to be a TV ad for some type of cold medicine, with the tag line, "A summer cold is a different animal..." ←Baseball Bugs ^{What's up, Doc?} carrots→ 05:23, 16 December 2016 (UTC)

Harvard Health Letter - Out in the cold says: "Research has shown that cold spells are reliably followed by upticks in the number of deaths from respiratory disease. Some of this may have to do with a few infectious organisms, like flu viruses, thriving in colder temperatures, but there's also evidence that exposure to cold temperatures suppresses the immune system, so the opportunities for infection increase. A study published in The New England Journal of Medicine in the late 1970s famously debunked the belief that the common cold is linked to cold exposure, but British cold researchers have maintained that there is a cold–to–common cold connection. Their hypothesis: cold air rushing into the nasal passages makes infections more probable by diminishing the local immune response there". Alansplodge (talk) 09:21, 16 December 2016 (UTC)

High Humidity Leads to Loss of Infectious Influenza Virus from Simulated Coughs: "At low relative humidity, influenza retains maximal infectivity and inactivation of the virus at higher relative humidity occurs rapidly after coughing. Although virus carried on aerosol particles <4 µM have the potential for remaining suspended in air currents longer and traveling further distances than those on larger particles, their rapid inactivation at high humidity tempers this concern. Maintaining indoor relative humidity >40% will significantly reduce the infectivity of aerosolized virus." Count Iblis (talk) 16:22, 16 December 2016 (UTC)