Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


hanson
Posts:
1,647
Registered:
12/13/04


602'214'162'949'382'947'882'374 is Avogadro's Number
Posted:
Aug 3, 2013 11:03 PM


"Sam Wormley" <swormley1@gmail.com> and "David Canzi" <dmcanzi@uwaterloo.ca> wrote: 158,962,555,217,826,360,000  Numberphile http://www.youtube.com/watch?v=G2_Q9FoDoQ http://www.youtube.com/watch?v=V4V2bpZlqx8 about... the construction, operation and code breaking of the the WWII German Enigma machine, Turing, Polish Bomba and the Allied's Xmachine. > hanson wrote: Bitch'n, guys. Now even more interesting and lasting is the legacy of an even large number: 602'214'162'949'382'947'882'374 or ~ 6E23 aka Avogadro's number ( N_A) in video http://www.youtube.com/watch?v=2dzS_LXvYA0 in which the dude talks about it "Avogadro's MOL or MOLE equivalent" that is used in chemistry, indicating that N_A # of atoms are what you see in 5 gallons of gas, or in 1/2 ounce of water, or in a hand full or dirt. > Missing though is the illustration of N_A vastness. > N_A not only relates to how many subsets (atoms) are in one set/bag (mole) of stuff, many fundamental physical constants are related in the same way: > k_Boltzmann * N_A = R_gas const (k for a single Atom) > (R for a mole of atoms) > Another such N_A sized quantum step is given by > e_elem.charge * N_A = Faraday constant (e for a single electron) > (F for a mole of electrons) > That jump of N_A is 6.02E23 orders of magnitude to get to get from a single atom to a handful (1 mole) of dirt is truly awesome: > That very N_A step is like telling ONE person what to do, and then to expect that (6E23/6E6) person in/of 10^17 earth sized populations (that's a Million Trillion Earths full of folks) will have heard and obey your command, and do what you have said to that one dingle person. > That is an illustration of how vast and powerful some laws of physics are... & they were all known long before 1905. > But N_A's influence does not stop there. N_A holds true the next step down into Planck's domain where it can be seen that 1 mole of Planck Length units = the size of the HBohr radius: l_pl * N_A *(pi*sqrt3) = r_H/mole ... or 1 mole of Planck Time units = the period of the Atomic time unit: t_pl *N_A*(pi*sqrt3/a) = Tau/mole ... or 1 mole of electron masses = the amount of a Planck Mass unit: m_e*N_A*(pi*sqrt3*a)= m_pl/mole > Remember that step from a single atom down into Planck's domain is again like the orderly behavior a Million Trillion earths full of folks who follow the order given to one single dude. > That then are the observations and experiences we get by taking 2 N_Asteps into the world of the "Tiny"... but N_A is also valid when making such steps upwards and out from our daily environment and looking at the celestial realm. We may catalog these N_A steps and say: > 1 N_A = #s of Planck length units within 1 HBohr radius. 2 N_A = #s of H2 in a few gals of whirling, contained gas. 3 N_A = #s of such gas vortexes in planetary systems. 4 N_A = #s of planetary systems within galaxies. 5 N_A = #s of galaxies within the observable universe. > These nested N_A situations exist due to the manifest self similarity in the natural world, including its fractal behavior that we encounter when's we step up or down Avogardro's N_A ladder. > The points presented above are NOT new. One can find ancient intuitive analogs in the Bhagavad Gita or in Jacob's ladder for the Bible beaters... ahahaha... > More contemporary versions were published by Dirac et.al. in his "Large Number Hypothesis" in the 1950s. > Caveat: All these speculations & notions, including the crap of SR & GR are mental masturbations and pipe dreams.. and will not by anyone even a singe cup of coffee... unless you can make a script from it and land a movie production for the SciFi channel.... ahahahahaha... Have at it and thanks for the laughs... hahahahanson



