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A335726 Mean radius of the orbit of the hydrogen atom's electron, in Bohr radii. 1
1, 3, 3, 7, 0, 3, 0, 1, 5, 6, 8, 6, 1, 7, 8, 0, 1, 5, 8, 9, 5, 6, 7, 2, 8, 6, 3, 2, 2, 9, 5, 8, 4, 7, 4, 9, 4, 8, 1, 1, 3, 9, 3, 8, 9, 7, 5, 1, 3, 9, 1, 1, 1, 3, 9, 0, 4, 3, 8, 5, 9, 4, 0, 9, 0, 6, 8, 7, 8, 2, 7, 7, 4, 5, 8, 4, 9, 5, 9, 2, 8, 8, 2, 2, 2, 6, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The wave function of the 1s orbital of the hydrogen atom is psi(r)=exp(-r/a0)/(sqrt(Pi*a0^3)) where a0 is the Bohr radius A003671. The radial distribution function is psi^2(r)*4*Pi*r^2 which then simplifies to 4*r^2*exp(-2r/a0)/a0^3. Integrating from 0 to infinity and finding the value R where the value inside is the same as outside yields a0 times the root of 2 + 4R + 4R^2 = e^(2R).

LINKS

Table of n, a(n) for n=1..87.

NIST, Fundamental Physical Constants: Bohr radius

Wikipedia, Classical electron radius

EXAMPLE

1.33703015686178015895672863229584749481139389751391113904385940906878277458....

MATHEMATICA

RealDigits[r /. FindRoot[2 + 4*r + 4*r^2 - Exp[2*r] == 0, {r, 3/2}, WorkingPrecision -> 100], 10, 87][[1]] (* Amiram Eldar, Aug 28 2020 *)

PROG

(PARI) solve(r=1, 2, 2+4*r+4*r^2-exp(2*r))

CROSSREFS

Cf. A335727, A003671.

Sequence in context: A066358 A261295 A118031 * A240504 A338775 A235162

Adjacent sequences:  A335723 A335724 A335725 * A335727 A335728 A335729

KEYWORD

nonn,cons

AUTHOR

Charles R Greathouse IV, Jun 19 2020

STATUS

approved

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Last modified December 8 00:04 EST 2021. Contains 349590 sequences. (Running on oeis4.)