Wikipedia:Reference desk/Archives/Science/2022 October 25

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October 25

what fungi is this?

what fungi is this?ℬ𝒜ℛ (talk) 17:03, 25 October 2022 (UTC)

ℬ𝒜ℛ (talk) 17:03, 25 October 2022 (UTC)

Do we know what type of tree this is? Many bracket fungi are specific to a particular host. Alansplodge (talk) 11:30, 26 October 2022 (UTC)

I'm pretty sure these are not bracket fungi for those are usually polypores which have pores instead of gills. In addition to their gills, adjacent to and to the left of the small grouping of round caps in the upper right corner of the picture there is a very small one lying on its side and it has a stem typical of the many species of gilled mushrooms. Modocc (talk) 16:03, 26 October 2022 (UTC)

Ah yes, I stand corrected. Alansplodge (talk) 16:23, 26 October 2022 (UTC)

User:Modocc and User:Alansplodge, I don't know what kind of tree it is, but I do know that the photo was taken in Snir Stream in the Golan Heights. ℬ𝒜ℛ (talk) 19:42, 26 October 2022 (UTC)

What is the acceleration of a molecule of gas as it collides with others?

Air molecules are traveling quite fast, and collide with each other, and walls very frequently. When an air molecule collides with another it might reverse direction completely, and when doing so it would experience quite a strong acceleration.

Any idea how much acceleration?

I could calculate it if I knew how long the collision took but I don't - I expect it would be perhaps like a spring, with the electrical repulsion of the electrons acting as non-linear springs. But I don't know how to calculate that. Ariel. (talk) 19:10, 25 October 2022 (UTC)

If you're talking about the behavior of a volume of gas, typically you'll be using the language of statistical mechanics to talk about average quantities, rather than the velocity or acceleration of a specific particle within the volume. The article on the Kinetic theory of gases is a good place to start for how those tools get built starting from the basic physics of inelastic collisions. PianoDan (talk) 20:02, 25 October 2022 (UTC)

If you're interested in the acceleration you'll have to look at the dynamics of molecular collisions. In full quantum detail I imagine this is a very hard problem. You may get an idea by solving the (Newtonian) equation of motion in the Lennard-Jones potential. I haven't been able to find the ε parameter for air, which is something you would need (should be on the order 1 kJ/mol). --Wrongfilter (talk) 20:08, 25 October 2022 (UTC)

So, nitrogen gas travels in the average or median, of 515 m/s in the STP. Are you asking how soon does it reach that speed after a collision? Also, when you say 2 gas molecules collide with each other, are you implying nucleus-to-nucleus collision, or electron-cloud to electron-cloud collision? 67.165.185.178 (talk) 22:58, 25 October 2022 (UTC).

Nucleuses would not collide in normal chemistry or room temperature physics, it's only in situations like in stars or supernovae that such things happen; and even in those cases, the situation is only every treated at the statistical mechanics level, not at the individual level. We thing of things like "cross-section" in nuclear reactions not as a physical area, but based on the likelihood of a successful interaction between nuclei on a statistical mechanics level. Indeed, thinking of individual particles on this level as behaving like little spheres in a Newtonian sense is rarely useful in making predictive models for the actual behavior of matter. If you're willing to hand wave individual behavior, the Boltzmann approach (statistical mechanics) is valid. If you want to model the particle-particle interactions, you need to use quantum mechanics. Thinking of atoms bouncing off of each other like hard spheres doesn't produce meaningfully useful results. --Jayron32 20:24, 26 October 2022 (UTC)

Suppose the width of the electron cloud is something like 60pm (picometers 10^12 of meter) and it is just atom to atom bouncing right back and they're going at 500 meters a second and it is bounced back nicely with a constant accelleration in 25 picometers. All of which are pretty unlikely but lets gets something of the order of what you might want. Then suppose the accelleration is a and it works for time t then at = 1000 m/s and at^2/2 = 25 pm so t/2 = 25x10^-12/1000 t = 50 x 10^-15 and a = 1000/(50 x 10^-15) = 20 x 1000/(1000 x 10^-15) = 20 x 10^15 m/s. So a fairly ginommous accelleration - you'd start approaching the speed of light within 300x10^6/20x10^15 = 15 nanoseconds. NadVolum (talk) 00:30, 26 October 2022 (UTC)

If the kinetic energy of the molecules in a gas is not very high, they bounce off of each other because of the repulsive force between their electron clouds, which is negligible at larger distances but gets high when they are close enough. The full story is complicated because of the Van der Waals force and the uneven distribution of electric charge in the electron clouds, which themselves change "shape" under the influence of the fields of a closely approximating other molecule, but to obtain a ballpark estimate by a back-of-the-envelope calculation we'll ignore this and simply consider the molecules as negatively charged point particles. After all, the typical distance between the molecules of a gas is huge compared to the size of the individual molecules, and for most of a molecule's journey between successive bounces the forces acting on the particle in the simplified point-particle model cancel largely out, so it will be coasting. This drastic simplification allows us to make another drastic simplification: just consider two equal particles approaching each other symmetrically on a straight line, bound for a heads-on collision at position $r=0.$ However, no collision will happen; it is prevented by their mutual repulsion, which makes them slow down and then rebound, eventually regaining their original speed but now in the opposite direction. Let's say they are coming in from far away with a speed $v=v_{\infty },$ slowing down by a repulsive force of the form $F=\kappa r^{{-}2}$ when their positions are given by $\pm r$, reaching velocity $v=0$ at position $r=\pm r_{0}.$ (The $\kappa$ is a constant of proportionality, to be defined later.) Because of the symmetry, we need to consider the fate of only one particle, say the one coming in from $r=+\infty .$ Its kinetic energy is given by $E_{\text{kin}}={\tfrac {1}{2}}mv_{2},$ where $m$ is the mass of a single particle. Its potential energy is given by $\textstyle {E_{\text{pot}}={-}\int Fdr=\kappa r^{{-}1}}.$

At $r=\infty ,$ $E_{\text{pot}}=0$, so the combined kinetic and potential energy $E=E_{\infty }={\tfrac {1}{2}}mv_{\infty }^{2}.$ At $r=r_{0},$ $E_{\text{kin}}=0$, so the combined energy $E=\kappa r_{0}^{{-}1}.$ By the law of conservation of energy, these two values are equal, so we can solve for $r_{0}$, giving us $r_{0}=\kappa E_{\infty }^{{-}1}.$ The acceleration given by $a=Fm^{{-}1}$ is maximal at $r=r_{0}.$ Combining this, we find for the maximal acceleration:

$a_{0}={\frac {E_{\infty }^{2}}{\kappa m}}.$

The average kinetic energy of a particle in a gas at temperature $T$ is given by ${\tfrac {3}{2}}k_{\text{B}}T,$ in which the Boltzmann constant $k_{\text{B}}\approx$ 1.38×10⁻²³ J⋅K⁻¹. At room temperature ($T=$ 293 K) we then get $E_{\infty }\approx$ 4×10⁻²¹ J. The repulsive force between two electrons is given by Coulomb's law; it equals $F=k_{\text{e}}e^{2}r^{{-}2},$ in which the Coulomb constant $k_{\text{e}}\approx$ 9×10⁹ N⋅m²⋅C⁻², and the elementary charge $e\approx$ 1.6×10⁻¹⁹ C. Assuming that the effective repelling charge "seen" by the approaching particle equals something like $2e,$ giving a factor of $4$ for the force, we can estimate the value of $\kappa$ as 9×10⁻²⁸ N⋅m². Using the average mass $m\approx$ 5×10⁻²⁶ kg of an air molecule (if I mode no calculation errors) then results in

$a_{0}\approx$ 3.5×10¹¹ m⋅s⁻².

 --Lambiam 11:27, 27 October 2022 (UTC)

I may be wrong about this but I'd have thought the nucleus would cancel the electrons at any great distance and when they repel it would be because their electron clouds were deformed or overlapped and no longer provided a shield for the nucleus so it is the positive charges of them which cause the repulsion. NadVolum (talk) 17:25, 27 October 2022 (UTC)

Some sources: [1], [2], [3].  --Lambiam 18:08, 27 October 2022 (UTC)

They seem to be saying the same as me, and it looks like the acceleration could be quite a bit higher as they are talking about a repulsion force proportional to 1/r^n where n is between 8 and 16 when the electron clouds start to interfere with each other. NadVolum (talk) 18:15, 27 October 2022 (UTC)

Indeed; especially the first source is explicit about the nuclei repelling each other. Wikipedia has an article on the Lennard-Jones potential. It should not be too difficult to redo the calculations with the parameters given there for argon, which are similar to those given in the third source for O₂. Basically, find $r_{0}$ by solving (numerically) $E_{\text{pot}}(r_{0})=E_{\infty }$ and next calculate $a_{0}$ by using $a=m^{{-}1}{\text{d}}E_{\text{pot}}(r)/{\text{d}}r.$  --Lambiam 08:13, 28 October 2022 (UTC)

Thanks very much for those references and particularly that last one which should give the result. Though I have some things to do and it would be pushing me a bit! :-) NadVolum (talk) 09:57, 28 October 2022 (UTC)

Unofficial atomic numbers

Is it sometimes appropriate to pretend that the atomic number of an element is something other than its usual atomic number?? The only example I can think of is hydrogen. Its atomic number is 1, but for the purpose of placing it in molecular compounds like ammonia, we treat it as if its atomic number were 7 1/2. Any other examples?? Georgia guy (talk) 23:39, 25 October 2022 (UTC)

We don't do that, not even with hydrogen. Changing the atomic number changes the number of protons, and therefore the element itself. Do you mean electrons? --OuroborosCobra (talk) 23:59, 25 October 2022 (UTC)

To understand what I mean, please note the rule for how binary molecular compounds work; specifically, the order the elements are written in. Usually, they're in column order with the lower element first if they're on the same column. But for this purpose, we treat hydrogen as if its atomic number were 7 1/2 rather than 1; that is, we put it between nitrogen and oxygen. Georgia guy (talk) 00:55, 26 October 2022 (UTC)

CHON. Is 6(1)(8)(7). So not COHN. 67.165.185.178 (talk) 01:26, 26 October 2022 (UTC).

That's irrelevant. We're talking about ordering elements in binary molecular compounds. Georgia guy (talk) 01:30, 26 October 2022 (UTC)

I frankly don't think the rule you're proposing actually exists. --Trovatore (talk) 01:33, 26 October 2022 (UTC)

If we're talking binary compounds, why does H need to be anything other than 1? "H₃N" is a fine way to write ammonia. Which "rule" are you considering? I don't know anyone that writes sulfur dioxide as "O₂S" (per the lower element first in same column idea you mention). But there are as many rules as you want. Sometimes we write a central atom followed by its surrounding atoms, so NH₃ and SO₂. Sometimes we write in order of electronegativity (the "cations then anions" way we name inorganics). Sometimes we write in Hill order. DMacks (talk) 01:36, 26 October 2022 (UTC)

The rule I think does kind-of-sort-of exist is that there's a generally tendency, not a rigid rule, to put the atoms in order of increasing electronegativity. That might (or might not) be why, for example, we write chlorine dioxide as ClO₂ rather than O₂Cl. That might partially explain why you see hydrogen more likely to be written later in the formula than you might expect for a Group I element. --Trovatore (talk) 01:39, 26 October 2022 (UTC)

It's idealised electronegativity per the Red Book, section IR-4.4.2.1. Elements are ordered by group, starting at 17 (most electronegative) and ending at 0 (least), and with all of La–Lu and Ac–Lr shoved under yttrium into group 3 in atomic number order. The exception is that hydrogen is treated as being between groups 16 and 15. (Technically this is incomplete since Cn–Og were not approved then yet, but it's fairly obvious where they would go, and in any case compounds of those are a rather niche use case). Double sharp (talk) 15:08, 26 October 2022 (UTC)

Hmm. That doesn't seem to explain ClO₂. --Trovatore (talk) 17:03, 26 October 2022 (UTC)

Oh, I just noticed that that's IUPAC — I have the impression that lots of IUPAC recommendations are simply ignored in practice as they should be, end editorial remark. --Trovatore (talk) 17:05, 26 October 2022 (UTC)

Well, some people even write F₂O. Actually so would I if I were making a comparison between it and H₂O. Double sharp (talk) 18:25, 26 October 2022 (UTC)

@Georgia guy I'm not surprised you are confused, since chemists and Wikipedia don't stick to a single convention. Take ammonia at Chemspider as an example. They write it as NH₃ but its molecular formula is in Hill order, as is usual for databases and hence H₃N. Similarly most chemists would write LiH for lithium hydride and that's how it is listed at Glossary of chemical formulae but in Hill order this is HLi and Chemspider use Li⁺ H^- for their simple drawing. So context matters. All I can say is that we don't ever say that hydrogen has an atomic number of 7 1/2 because that's certainly incorrect! Mike Turnbull (talk) 15:09, 26 October 2022 (UTC)

I am intrigued. I've never really wondered before why we have H₂O rather than OH₂, is there some good reason for thsi? NadVolum (talk) 16:08, 26 October 2022 (UTC)

H is less electronegative than O. So it makes sense if you want the partial positive charges to the left. Double sharp (talk) 18:26, 26 October 2022 (UTC)

Yeah, but ammonia is traditionally written NH₃. And H is also less electronegative than nitrogen. I suspect that the real answer is that H atoms that can act as Bronsted acids are usually written at the front of a formula, whereas H atoms that cannot are usually written later in the formula. Thus H₃O⁺, H₂O, but OH^-. Both hydronium and water can act as Bronsted acids, but in hydroxide, it cannot. It is only in extreme situations that ammonia acts as a Bronsted acid. On the converse to that argument is that ammonium is almost always written NH₄⁺, and yet is a very good Bronsted acid. Ultimately, chemistry nomenclature is a language. It's a highly specialized language (a jargon, if you will), and as a language, it is subject to the same irregularities as any language. Historical artifacts, linguistic drift, all of that happens in chemistry nomenclature as it does in any language. Some organizations (like IUPAC) have attempt to create an artificially "perfectly regular" system of nomenclature, but these have been equally as ignored by working chemists as have other conlangs by humanity at large. Chemists will use the language of chemical nomenclature as it has evolved in the community organically, and will continue to have these kinds of irregularities in the system. --Jayron32 20:18, 26 October 2022 (UTC)

Thus confirming the superiority of organic over inorganic chemistry:) DMacks (talk) 20:47, 26 October 2022 (UTC)

Re OH⁻, my vague impression is that it's more common to see the HO order for the radical (•HO) than the anion. Though I might be completely wrong about that. Double sharp (talk) 22:27, 26 October 2022 (UTC)

Regarding the radical; the Wikipedia article writes it as •OH, and notes explicitly that the • goes next to the O, so if written in reverse order (which is common in mechanism diagrams depending on the location of the formulae, for example) it would be written HO•. However a google search, which has several scholarly papers, shows that •OH is commonly used. --Jayron32 23:29, 26 October 2022 (UTC)

• Regarding the original question: Atomic number is always, only, and every time, without exception defined as the number of protons in the nucleus. Half a proton is a meaningless thing, so that's a red flag that something must be wrong with the OP's assumptions. Also, as every element is defined by the number of protons it has in its nucleus, hydrogen can only every have exactly 1 proton (if it had 2 a different number of protons, it'd not be hydrogen!) so since 1 proton means hydrogen, and atomic number always equals the number of protons, hydrogen can only have an atomic number of 1. QED. --Jayron32 23:33, 26 October 2022 (UTC)

  As impossible as an atomic number of 7 1/2 is hydrogen is last in binary hydrides till atomic number 7 then first for hydrogen oxide and hydrogen fluoride (CH4 NH3 H2O HF). There's the grain of not complete nonsense. But of course binary hydride order correlates better with group number not atomic (SiH4 PH3 H2S HCl HBr HI). Sagittarian Milky Way (talk) 04:09, 27 October 2022 (UTC)

  Hydrogen telluride H₂Te vs polonium hydride PoH₂ is a fun pair. DMacks (talk) 05:35, 27 October 2022 (UTC)