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September 7

Distance of electron from Hydrogen Nucleus

I have another question from my inorganic textbook. From reading the text, I more or less know what they want me to say. In its ground state, hydrogen's single electron will be in the 1s orbital. The answer to a) is that the electron's most probable location is where the radial probability density is highest (i.e. the square of the radial wave function). From this graph in the text (where the radial probability density is denoted R²), it's clear that the highest probability is at the nucleus itself. For part b) the question is asking about the radial distribution function (drawn in red in the same graph), which has a maximum at the point equal to the Bohr radius (52.9pm) on the nuclear charge (1 for hydrogen, so the answer is 52.9pm). Even though I'm pretty sure I know what they want me to say, I don't understand what it means. How can the most probable distance be 52.9pm from the nucleus when the most probable location is the nucleus itself? What does that actually mean? Is it something like "The most probable distance is 52.9pm in any direction from the nucleus, so the most probable location is the average of those points i.e. in the center"?

Also, the text gives me this relationship for determining the maximum of the radial distribution function. But it only seems to be for 1s electrons. The accompanying text notes that the number should be higher for higher n values, but there's nowhere to actually plug in n, and I need to determine the value for n=2 to solve part c) What is the most probable distance of a 2s electron from the nucleus? 202.155.85.18 (talk) 09:31, 7 September 2018 (UTC) EDIT: Actually, they also give me this graph in the text. Perhaps I'm just supposed to read off that the maximum of a 2s orbital's radial distribution function is a tiny bit over 2x the Bohr radius and leave it at that? Googling around there are some tutorials for physics students explaining how to actually determine the 2s RDF numerically and then find the maximum, but I'm fairly sure I'm not meant to be able to do that given this passage in the text. 202.155.85.18 (talk) 09:41, 7 September 2018 (UTC)[reply]

this page has a discussion of the derivations of the various radii in question. --Jayron 32 11:32, 7 September 2018 (UTC)[reply]

Mistake in article

In Apollo 11, it says "Aldrin joined him about 20 minutes later". In Buzz Aldrin: "Aldrin set foot on the Moon at 03:15:16 on July 21, 1969 (UTC), 9 minutes after Armstrong first touched the surface".111.235.89.222 (talk) 11:34, 7 September 2018 (UTC)[reply]

I reviewed the details, and I'm comfortable with using the vague language, "about 20 minutes later," because the article introduction is only providing an abbreviated summary.

One of the best resources for factual details of the Apollo lunar missions is the Apollo Lunar Surface Journal. Here's the transcript for Armstrong and Aldrin during the first extravehicular activity on the moon's surface.

Ultimately, both astronauts got on the moon within "about" twenty minutes, depending on how you count - the procedures for the very first moon landing were complicated. The process of exiting the Lunar Module - just "walking out the door" - actually took several minutes. Here are Page 40 and Page 41 of the EVA checklist.

I think it's alright for our article's lead paragraph to say "twenty minutes" - readers who want more details about precisely what was going on during that time can find such details in the rest of the article and in the primary sources referenced by the article. Nimur (talk) 14:13, 7 September 2018 (UTC)[reply]

I looked at the Lunar Surface Journal (linked above), and Armstrong stepped onto the Moon at about 109:24:20, mission elapsed time. Aldrin is on the LM footpad about 109:42, but he sets foot on the Moon about 109:44, so "20 minutes later" is good. Bubba73 ^{You talkin' to me?} 15:43, 7 September 2018 (UTC)[reply]

Efficient swimming: horizontal or vertical fin

Does it make any difference, even if it's a small one, whether a marine animal (imagine dolphin vs shark) has its tail fin attached horizontally or vertically? Obviously, there's an ergonomic difference. Humans will have a hard time flapping a fin horizontally. I ask discounting such issues. --Doroletho (talk) 13:50, 7 September 2018 (UTC)[reply]

Without addressing the more general scenario I would observe that, close to the surface, a horizontal fin (i.e. one moving up and down) could waste some of its energy by causing splashes where a vertical (side-to-side) fin would not. However, IANAHydrodynamicist. {The poster formerly known as 87.81.230.195} 2.122.60.253 (talk) 14:56, 7 September 2018 (UTC)[reply]

Ignoring issues of when fish break the surface or when they are skimming the bed, the orientation of the caudal fin (tail fin) is irrelevant. It isn't about orientation. It is about movement. Fish flex side-to-side, not up and down. It is how the spine and muscles are arranged. Sea mammals flex up and down, so they have horizontal fins. 216.59.42.36 (talk) 15:43, 7 September 2018 (UTC)[reply]

I think it evident that Doroletho knows this, and addressed it by mentioning ergonomics. I understand the query to be whether there is any inherent propulsive advantage, assuming perfected body design in either case, of a vertical tail fin over a horizontal one or vice-versa. I would have thought not, but as previously mentioned IANAH.

It occurs to me that one circumstance where it might make a difference is if our hypothetical entity needs to change directions more often or more quickly in a horizontal plane (changing direction) or a vertical one (diving or ascending), since a caudal fin is generally larger, stronger and (by virtue of its position) has more leverage than more "inboard" fins like pectoral, pelvic, etc.

Our articles Fish locomotion and Aquatic locomotion might contain material of some relevance. {The poster formerly known as 87.81.230.195} 2.122.60.253 (talk) 19:24, 7 September 2018 (UTC)[reply]

Animals that need to surface and dive have horizontal tails for the movement to and from the surface. Animals that breathe underwater have vertical tails. — Preceding unsigned comment added by 68.191.203.98 (talk) 21:07, 7 September 2018 (UTC)[reply]

It would be a mistake to attribute all of this to what makes the most sense given an animal's lifestyle, without considering evolution, as was discussed above you. It makes just as much sense for lifestyle to follow from forms and functions that are already available. Fish spines flex in the left-right axis, while mammalian spines flex in the dorsal-ventral axis. There are fish with horizontal tails, from the perspective of someone perpendicular to the ground: flatfish. They actually move with one side facing down, and one facing up, but their bodies are strikingly asymmetrical in the left-right axis, giving a functional top and bottom. Someguy1221 (talk) 22:42, 7 September 2018 (UTC)[reply]

Googling the subject indicates that the fastest fish are faster than the fastest mammals - but not by a whole lot. ←Baseball Bugs ^{What's up, Doc?} carrots→ 23:53, 7 September 2018 (UTC)[reply]

I think the fastest species in water is the Marlin, reaching speeds of up to 80 km/h (50 mph). They have a very thin, long body tho, so it would be unfair to compare them with the much more "bulky" Dolphins, who manage 55 km/h (35 mph) with different fins. In fluid dynamics it does not make a difference. Besides Dolphins are so smart, they would probably start swimming tilted to 90 degrees if that would give them a speed advantage. --Kharon (talk) 07:04, 9 September 2018 (UTC)[reply]