A335726 Mean radius of the orbit of the hydrogen atom's electron, in Bohr radii.

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

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 A359407

Adjacent sequences: A335723 A335724 A335725 * A335727 A335728 A335729

Keyword

nonn,cons

Author

Charles R Greathouse IV, Jun 19 2020

Status

approved