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u/HAL9001-96 1d ago
not quite
now they do probably mean logarithmically speaking
and specks of dust come in very differnet sizes
and hte size of an atom is ab it tricky to define
but we're talking something like 10^-11 to 10^-9 meters and about 10^7m so the middle is about 10^-2 to 10^-1 meters so about 1-10 cm
now an atoms core would only be abut 10^-15 to 10^-14 meters putting the middle to about 10^-4m or 0.1mm which is a relatively large dust particle but in the right range
but while that depiction of an atom is a bit of an inaccurate simplification anyways it clearly shows a whole atom, not a nucleus
also, of course, linearly rather htan logairthmically speaking the middle between an atom and hte earth in diameter would be a planet half hte size of the earth so roughly mars
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u/Futuressobright 1d ago
So would it be right to say if an atom were the size of a speck of dust a speck of dust would be the size of the earth?
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u/HAL9001-96 1d ago
no
going form an atom to a large speck of dust would be going from about 10^-10 to about 10^-4 so about a factor 1 million
go another factor one million and oyu are at 10^2, only 100 meters
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u/Bright-Historian-216 1d ago
yeah, if i understand it correctly you would need to increase each 10 billion times their size.
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u/KosmosKlaus 1d ago
Or maybe a golf ball is roughly in the middle of an atom and the earth
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u/NetworkSingularity 1d ago
On a logarithmic scale, specifically. On a regular old linear scale it’s Mars, as someone else said
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u/chroniclerofblarney 1d ago
You should just switch the H and T keys on your keyboard at this point.
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u/488302020 1d ago
noh quihe
now htey do probably mean logarihtmically speaking
and specks of dush come in very differnet sizes
and the size of an ahom is ab ih hricky ho define
but we’re halking somehting like 10-11 to 10-9 mehers and abouh 107m so hte middle is abouh 10-2 to 10-1 mehers so abouh 1-10 cm
now an ahoms core would only be abuh 10-15 ho 10-14 mehers puhhing hte middle ho abouh 10-4m or 0.1mm wtict is a relahively large dush parhicle buh in hte rigth range
buh wtile htah depichion of an ahom is a bih of an inaccurahe simplificahion anyways ih clearly stows a wtole ahom, noh a nucleus
also, of course, linearly rahter than logairhtmically speaking hte middle behween an ahom and the earht in diameher would be a planeh talf the size of hte earht so rougtly mars
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u/Mcipark 1d ago
Yeah haha, a 1/2 slice of the earth is halfway between an atom and the earth, a speck of dust is not.
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u/HAL9001-96 1d ago
well log scale it.. almost is sortof
or linearly you ight call it "rootway between"
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u/tico600 1d ago
Missed an occasion to compare to a grain of sand then, because 0.1mm would totally be the right size
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u/HAL9001-96 1d ago
also varies in size, similar ot a grain of dust which means the picture would be equally wrong for both
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u/tico600 1d ago
Of course it varies, but wouldn't a 0.1mm grain of sand make much more sense than a speck of dust ?
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u/HAL9001-96 1d ago
I already used the upper end of dust at 0.1mm as well
go any lower tha nthat which both dust and sand do at times and it gets even worse
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u/Ok_Zebra_1500 1d ago
There was a public radio episode that also estimated 10^-2 or so. Large single celled organism IIRC.
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u/HAL9001-96 1d ago
10^-2 m is 1cm, thats very much visible everyday scale
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u/Ok_Zebra_1500 1d ago
I did not say you couldn't see it just the size of a large single celled organism. Large bubble algae or small plasmodial slime mold.
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u/HAL9001-96 1d ago
technically yeah but thats just becuase some single celled organisms can be surprisingly big, its certianly not hte first comparison I'd go for for something the isze of a fingernail
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u/Centaurus3850 1d ago
interesting… i don’t understand this at all…
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u/Ingraved 1d ago
Not accurate.
Earth (E) ~1.2 x 10 ^(7) m
Dust (D) ~ 2.5 x 10 ^(-6) m
Atom (A) ~ 1 x 10 ^(-10) m
E-------------D----A
A crude scale.
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u/DeltaAlphaGulf 1d ago
Whats halfway between an electron and the galaxy or the observable universe?
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u/zrice03 1d ago
Well, we don't know the radius of an electron, assuming it's not an actual point particle. Though we do know it's less than 10^-22 m, so we'll just use that. Our galaxy is 100,000 LY across, or 9.46 x 10^20 m. The observable universe has a radius of about 46.5 billion LY, or 4.4 x 10^26 m.
Halfway between an electron and the galaxy would be 0.307 meters, or about just about 1 foot. Halfway between an electron and the observable universe would be 200 meters.
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u/shaonafle21 1d ago
A human egg is halfway between the plank length and observable universe.
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u/gorka_la_pork 1d ago
I'd heard it was a brain cell, but either way that means we're bigger than average :D
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u/sOrdinary917 1d ago
Linearly speaking, = half a galaxy plus half an electon. Approx = half a galaxy
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u/Tryingtoknowmore 1d ago
Could I get this scale for where Humans are between the Planck length and the observable universe? I've heard we too are about halfway between them.
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u/Ingraved 1d ago
Observable Universe (O) 8.8 x 10 ^( 26) m
Human Adult Height (H) 1.7 x 10 ^( 0 ) m
Planck Length (P) 1.6 x 10 ^(-35) m
Center Line (|)O----------------------------H--|-------------------------------P
Crude ScaleClose, only off by a kilometer... You could only fit like 1 billion people in a kilometere sized sphere...
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u/Tryingtoknowmore 1d ago
Thank you for the calculation and the hamster ball of death reference. Learning is never disappointing.
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u/Sunfried 1d ago
So I get halfway as 3.5 x 10-2 m, or 3.5cm. So the middle object could be a chicken nugget.
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u/qrpc 2✓ 1d ago
That is a picture of a lithium atom with an atomic radius of about 0.000000000105 meters. The radius of the earth is 6,378,137 meters. The midpoint between nearly zero and 6.4 million is around 3.2 million meters.
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u/PESSSSTILENCE 1d ago
this is the correct answer, they tried to mean logarithmically but like.. its a linear question as far as i can tell
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u/MonitorPowerful5461 1d ago
They mean logarithmically
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u/UniqueUsername014 1d ago
maybe they think that, but what they said has a very different meaning
the object halfway between the size of the earth and an atom definitely has the size of half an earth
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u/vwibrasivat 1d ago
It's wrong in every possible way, including "They mean logarithmically".
(reporting diameters)
Smallest salt grain is 0.2 millimeters. = 2.0x10-4 m
Lithium atom (shown) is 304 picometers = 3.04 x 10-10
The ratio is 6 orders of magnitude. 106
Earth diameter is 1.2742018 × 107 meters
Ratio of (earth):(salt grain) is 11 orders of magnitude 1011
log_base_10 would report that 6 not equal 11.
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u/Apart_Astronomer9944 1d ago
Not sure about this but.. Size of earth is about 106 m Size of an atom is 10-10 Size of dust is according to google 10-6 So no about a third of the way
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u/soyalguien335 1d ago
An atom has a size of around 0.1nm Earth has a diameter or more than 10000km In meters that means 10-10 and 107 The geometric average of both is roughly 10-1.5 meters or 3 centimeters, which is more than the diameter of a ping pong bal, much much bigger than a speck of dust of 0.2 milimeter.
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u/Striking_Credit5088 1d ago
That'd have to be one hell of a speck of dust.
A lithium atom (likely what's depicted) is about 2 · 10-10 m
Earth is 1.3 · 107 m
Something halfway between would be about 6,371 kilometers wide, the approximate size of Russia
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Another way to look at it is that a speck of dust is about 50,000 times the size of an atom, while earth is more than a trillion times the size of a speck of dust.
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u/MonitorPowerful5461 1d ago
They mean logarithmic, not linear, scale
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u/Striking_Credit5088 1d ago
Oh well if you take the geometric mean of ( 2 · 10-10 m · 1.3 · 107 m)1/2 = 5.1cm or about the size of an apple.
Still one hell of a speck of dust.
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u/Icy_Sector3183 1d ago
No.
An atom is about 1e-10 m in diameter, a speck of dust is about 1e-5 m, and the earth is about 1,2e7 m in diameter.
If you just look at the degrees of magnitude atom -> dust is x 10 000, and dust -> earth is x 1 000 000 000 000.
You'll need to put in some more work to explain how the speck of dust is halfway between an atom and the earth.
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u/Instructor_Alan 1d ago
Atom is roughly 10-10 m (1 Ångstrom), a speck of dust is 10-4 m (100 μm), and Earth's diameter is roughly 1.2*107 m (12000 km). So not exactly halfway but close.
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u/Busalonium 1d ago
I'm not sure how you'd define halfway between to get that answer. I think a conventional understanding of halfway between an atom and the earth would give you something that is half the size of earth.
My first thought was maybe it's about orders of magnitude. But just looking at the order of magnitude in metres;
Atoms: 10-10 Earth: 106
So anything halfway between there would be 10-2 metres.
According to this site
https://www.engineeringtoolbox.com/particle-sizes-d_934.html
Dust is smaller than that and the only thing on that list that big is gravel.
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u/bartekltg 1d ago
If 'halfway' is on the logarithmic scale (cant be on linear, it would be just half of the earth;) ) it rather a small pebel. ~4cm (taking the diameter of the carbon atom)
https://www.wolframalpha.com/input?i=sqrt%28diameter+of+earth+*+diameter+of+carbon+atom%29
If we take diameter of only the nucleus, we are closer, 0.24mm
https://www.wolframalpha.com/input?i=sqrt%28diameter+of+earth+*+diameter+of+carbon+atom+nucleus%29
This already can be qualified as dust, on the bigger part of the scale. But the picture is wrong, we have to take the size of only the nucleus, not the whole atom.
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u/vwibrasivat 1d ago
It's wrong in every possible way, including "he means logarithmically".
(reporting diameters)
Smallest salt grain is 0.2 millimeters. = 2.0x10-4 m
Lithium atom (shown) is 304 picometers = 3.04 x 10-10
The ratio is 6 orders of magnitude. 106
Earth diameter is 1.2742018 × 107 meters
Ratio of (earth):(salt grain) is 11 orders of magnitude 1011
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u/FIicker7 1d ago
What object would be halfway between the two?
A golf ball or baseball or a bowling ball?
Just curious
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u/transguy357 1d ago
I mean it depends what kind of halfway you’re talking about. The arithmetic mean of the masses of a Lithium atom and the Earth is 2.986x1027g.
(A Lithium atom’s mass is 1.153x10-23g according to google. The Earth’s is 5.972x1027kg.)
The geometric mean is a more likely calculation which is basically half way between them in terms of orders of magnitude. My calculator gives this at 262g, which is closer but certainly not the mass of a speck of dust.
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u/KosmosKlaus 1d ago
Are you saying that Mars is in the middle between an atom and earth in size?
That seems like nonsense 🤷🏻♂️
Mars is half the size of Earth, but way more than double the size of an atom
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u/CybershotBs 1d ago
Linearly speaking definitely not, even if an atom had size 0 the middle between 0 and the earth would be half the earth
Logarithmically speaking, other comments have answered
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u/Aeon1508 1d ago
I remember hearing at some point that The size of the smallest known particle relative to humans is the same as the size of human relatives to the observable universe. Or something like that
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u/TeririHerscherOfCute 1d ago
by volume, absolutely no, by scale, sure, but scale means nothing in a universe where the entire planet we live on makes up less than 0.00000000000000001% of it's total mass
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u/ADMINISTATOR_CYRUS 1d ago
In terms of logarithms, maybe that's what they meant but it's a bit off I think.
Size of the earth is around 106 m.
Size of dust is 10-6
Size of an atom is 10-10
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u/Laffenor 20h ago
All of these comments with massive numbers discussing whether it is 1/3 or 1/4 the way between the earth and an atom.
The formula to find what is half way between the size of an atom and earth (let's call it X) should be this (A = size of atom E = size of earth)
X = (E - A)/2 + A.
So if we say that the diameter of earth is 12 756km and the diameter of an atom is 0km, the spec of dust in question has a diameter of 6 378km. That's larger than even the biggest dust bunny in the farthest corner under the basement sofa of most homes.
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u/Specialist-Two383 20h ago
I like this sort of comparison. It's like how the breadth of a hair is as small compared to the Hubble scale as the Planck scale is to the breadth of a hair. So it's sort of the middle scale of the universe.
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