Wikipedia:Reference desk/Archives/Science/2024 September 7

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September 7

Dilithium in real life

The article about real-life dilithium has the potential to be quite interesting, but because of search result overlap with the Star Trek substance, it's difficult to nail down references on this topic. We could use some to establish - for example - if it's a gas at standard temperature and pressure, and if it's "stable", what its typical lifetime is. I would be interested if anyone could put their fingers on sources with this sort of info. -- Beland (talk) 08:22, 7 September 2024 (UTC)

IIRC all the alkali metal dimers are known in the gas phase (not sure how much of the vapour is monatomic vs diatomic, though). But they will condense back into metallically bonded structures when cooled below the boiling point. Double sharp (talk) 08:25, 7 September 2024 (UTC)

@Beland The general way to find decent references is to use Google Scholar. This search is a start and removes some hits from articles about a piece of software called dilithium by searching for co-occurence of that word with "lithium". Mike Turnbull (talk) 11:05, 7 September 2024 (UTC)

You can also search in a standard search engine using its InChIKey, SMBQBQBNOXIFSF-UHFFFAOYSA-N Mike Turnbull (talk) 11:11, 7 September 2024 (UTC)

The search term "lithium dimer" also seems to work well. Double sharp (talk) 12:19, 7 September 2024 (UTC)

Excellent; thanks for the tips! -- Beland (talk) 16:28, 7 September 2024 (UTC)

Colour of radiation glow

The description of this picture of actinium states that the blue comes from Cherenkov radiation, but I'm not sure can Cherenkov radiation produces other colours. --Nucleus hydro elemon (talk) 11:27, 7 September 2024 (UTC)

Actinium glows blue, curium glows purple, while radon glows yellow. What decides the glow colour of a radioactive element? Nucleus hydro elemon (talk) 11:27, 7 September 2024 (UTC)

Radioactive elements and their isotopes release, for example, alpha particles of various energies. These ionise surrounding material and the colours come from the ions relaxing back to their ground states. There is a chart which gives the energies (zoom in to the isotope of interest). Mike Turnbull (talk) 12:16, 7 September 2024 (UTC)

Two things about the image-caption details. First, our Cherenkov radiation article discusses the origin of the color via the Frank–Tamm formula. Second, is the glow from Cherenkov radiation or simple ionization? The linked image's description page says "the Cherenkov blue glow that originates from the ionization of surrounding air by alpha particles", which sounds like it's conflating those two. File:Actinium_sample_(31481701837).png's description, also from ORNL sources, simply says "ionization of surrounding air by alpha particles." DMacks (talk) 05:25, 9 September 2024 (UTC)

Effect of elevation on sunshine

Sunshine duration says that locations on the Arctic Circle get 4,647 hours of sunshine (disregarding the effects of clouds), the most of any location worldwide due to the effects of atmospheric refraction. Imagine that Surtsey-type eruptions produce a new mountain in an ocean location on the Arctic Circle, and it's extremely high — say, 5000m. Disregarding the effects of clouds, will it get much more sunshine than locations at sea level? I assume it will get some more than those locations, since the sun's above the horizon longer for an elevated location, but I don't know how much longer. Nyttend (talk) 21:49, 7 September 2024 (UTC)

It doesn't have to be on the Arctic Circle, you could build a (thought experiment) 100,000 km tall tower on the Equator, and as the Earth rotated, the top of the tower would only briefly be in Earth's shadow, if at all. Abductive (reasoning) 05:14, 8 September 2024 (UTC)

Let $R\approx 6378\,{\text{km}}$ denote the radius of the Earth (taken to be a sphere) and let $\varepsilon \approx 23.44^{\circ }$ stand for the obliquity of the ecliptic. Then, for the top of a tower erected at latitude $\phi$ to avoid the shadow cast by the earth day and year around, its height should be at least $R(|\csc(\varepsilon \,{\dot {-}}\,|\phi |)|-1),$ where $a\,{\dot {-}}\,b=a-b~{\text{if}}~a\geq b,$ and equals zero otherwise. [edited 11:27, 9 September 2024 (UTC); edited again 11:56, 10 September 2024 (UTC)]

• At the Poles, with $|\phi |=90^{\circ },$ this comes out at about $574\,{\text{km}},$ a mere 700 Burj Khalifas stacked on top of each other. This is the height of a Low Earth orbit, so the tower may be hit by satellites in polar orbit.
• On the Arctic Circles, with $|\phi |=90^{\circ }-\varepsilon ,$ the tower needs to be $2953\,{\text{km}}$ high.
• In the tropics, from the Tropic of Cancer to the Tropic of Capricorn, where $|\phi |\leq \varepsilon ,$ the tower needs to be infinitely high, which is impractical from an engineering point of view :).

 --Lambiam 09:40, 8 September 2024 (UTC)

I dunno if that makes sense. Consider Saturn's rings; they are often (always?) partly in shadow. But a tower on the axis will stick out into perpetual sunlight at a height much less than the rings. Abductive (reasoning) 14:55, 8 September 2024 (UTC)

I must have made a mistake; if $\varepsilon$ had been zero (meaning that the equatorial and ecliptic planes coincide), any tower at a pole would always be in sunlight. Possibly, the fix is simply to replace $\sec$ by $\csc .$ I can't examine this further right now.  --Lambiam 17:52, 8 September 2024 (UTC) — Now corrected and hopefully now correct.  --Lambiam 11:27, 9 September 2024 (UTC)

But wait a minute. If at some point in the year the sun is directly overhead at noon (i.e. between the two tropics) then if the tower is normal to the geoid it's going to have to be very long, because at midnight sun-earth-tower form a straight line. This is analogous to a total solar eclipse, where the straight line is sun-moon-earth. But you can have annular eclipses because the sun is so much larger than the moon, and when the moon is beyond a certain distance we can "see over it" and catch a glimpse of the sun. As the sun is much bigger than the earth, the earth's shadow is not infinitely long and at some point the top of the tower must emerge from the gloom. 2A00:23D0:CCD:CE01:1197:733B:D027:4118 (talk) 15:27, 9 September 2024 (UTC)

Just like my calculation assumed a spherical Cow Earth, it assumed an infinitely distant Sun. Since we have total lunar eclipses, we know the Earth's shadow extends to far beyond the Moon's orbit. Ignoring the effect of sunlight being bent by our atmosphere, the shadow cone extends to 1.38 Tm, almost 1/100 of an astronomical unit.  --Lambiam 11:56, 10 September 2024 (UTC)