“In any molecular system consisting of positive nuclei and electrons in which the nuclei are at rest relative to each other and the electrons move in circular orbits, the angular momentum of everyelectron round the centre of its orbit will in the permanent state of the system be equal to,whereis Planck’s constant”[22].
In analogy with the considerations onp. 23, we shall assume that a configuration satisfying this condition is stable if the total energy of the system is less than in any neighbouring configuration satisfying the same condition of the angular momentum of the electrons.
As mentioned in the introduction, the above hypothesis will be used in a following communication as a basis for a theory of the constitution of atoms and molecules. It will be shown that it leads to results which seem to be in conformity with experiments on a number of different phenomena.
The foundation of the hypothesis has been sought entirely in its relation with Planck’s theory of radiation; by help of considerations given later it will be attempted to throw some further light on the foundation of it from another point of view.
April 5, 1913.
[1]Communicated by Prof. E. Rutherford, F.R.S.
[1]Communicated by Prof. E. Rutherford, F.R.S.
[2]E. Rutherford, Phil. Mag. xxi. p. 669 (1911).
[2]E. Rutherford, Phil. Mag. xxi. p. 669 (1911).
[3]See also Geiger and Marsden, Phil. Mag. April 1913.
[3]See also Geiger and Marsden, Phil. Mag. April 1913.
[4]J. J. Thomson, Phil. Mag., vii. p. 237 (1904).
[4]J. J. Thomson, Phil. Mag., vii. p. 237 (1904).
[5]See f. inst., ‘Théorie du rayonnement et les quanta.’ Rapports de la reunion à Bruxelles, Nov. 1911. Paris, 1912.
[5]See f. inst., ‘Théorie du rayonnement et les quanta.’ Rapports de la reunion à Bruxelles, Nov. 1911. Paris, 1912.
[6]See f. inst., M. Planck,Ann. d. Phys. xxxi. p. 758 (1910); xxxvii. p. 642 (1912);Verh. deutsch. Phys. Ges. 1911, p. 138.
[6]See f. inst., M. Planck,Ann. d. Phys. xxxi. p. 758 (1910); xxxvii. p. 642 (1912);Verh. deutsch. Phys. Ges. 1911, p. 138.
[7]A. Einstein,Ann. d. Phys. xvii. p. 102 (1905): xx. p. 199 (1906); xxii. p. 180 (1907).
[7]A. Einstein,Ann. d. Phys. xvii. p. 102 (1905): xx. p. 199 (1906); xxii. p. 180 (1907).
[8]A. E. Haas,Jahrb. d. Rad. u. El. vii. p. 261 (1910). See further, A. Schidlof,Ann. d. Phys. xxxv. p. 90 (1911); E. Wertheimer,Phys. Zeitschr. xii. p. 409 (1911),Verh. deutsch. Phys. Ges. 1912, p. 431; F. A. Lindemann,Verh. deutsch. Phys. Ges. 1911, pp. 482, 1107; F. Haber,Verh. deutsch. Phys. Ges. 1911, p. 1117.
[8]A. E. Haas,Jahrb. d. Rad. u. El. vii. p. 261 (1910). See further, A. Schidlof,Ann. d. Phys. xxxv. p. 90 (1911); E. Wertheimer,Phys. Zeitschr. xii. p. 409 (1911),Verh. deutsch. Phys. Ges. 1912, p. 431; F. A. Lindemann,Verh. deutsch. Phys. Ges. 1911, pp. 482, 1107; F. Haber,Verh. deutsch. Phys. Ges. 1911, p. 1117.
[9]J. W. Nicholson, Month. Not. Roy. Astr. Soc. lxxii. pp. 49, 139, 677, 693, 729 (1912).
[9]J. W. Nicholson, Month. Not. Roy. Astr. Soc. lxxii. pp. 49, 139, 677, 693, 729 (1912).
[10]See f. inst. N. Bohr, Phil. Mag. xxv. p. 24 (1913). The conclusion drawn in the paper cited is strongly supported by the fact that hydrogen, in the experiments on positive rays of Sir J. J. Thomson, is the only element which never occurs with a positive charge corresponding to the loss of more than one electron (comp. Phil. Mag. xxiv. p. 672 (1912)).
[10]See f. inst. N. Bohr, Phil. Mag. xxv. p. 24 (1913). The conclusion drawn in the paper cited is strongly supported by the fact that hydrogen, in the experiments on positive rays of Sir J. J. Thomson, is the only element which never occurs with a positive charge corresponding to the loss of more than one electron (comp. Phil. Mag. xxiv. p. 672 (1912)).
[11]F. Paschen,Ann. d. Phys. xxvii. p. 565 (1908).
[11]F. Paschen,Ann. d. Phys. xxvii. p. 565 (1908).
[12]E. C. Pickering, Astrophys. J. iv. p. 369 (1896); v. p. 92 (1897).
[12]E. C. Pickering, Astrophys. J. iv. p. 369 (1896); v. p. 92 (1897).
[13]A. Fowler, Month. isot. Kov. Astr. Soc. lxxiii. Dec. 1912.
[13]A. Fowler, Month. isot. Kov. Astr. Soc. lxxiii. Dec. 1912.
[14]W. Ritz,Phys. Zeitschr. ix. p. 521 (1908).
[14]W. Ritz,Phys. Zeitschr. ix. p. 521 (1908).
[15]J. W. Nicholson,loc. cit. p. 679.
[15]J. W. Nicholson,loc. cit. p. 679.
[16]A. Einstein,Ann. d. Phys. xvii, p. 146 (1905).
[16]A. Einstein,Ann. d. Phys. xvii, p. 146 (1905).
[17]R. W. Wood, Physical Optics, p. 518 (1911).Phil. Mag. S. 6. Vol. 26. No. 151.July1913.
[17]R. W. Wood, Physical Optics, p. 518 (1911).Phil. Mag. S. 6. Vol. 26. No. 151.July1913.
[18]Compare J. J. Thomson, Phil. Mag. xxiii. p. 456 (1912).
[18]Compare J. J. Thomson, Phil. Mag. xxiii. p. 456 (1912).
[19]E. Rutherford,Phil. Mag. xxiv. pp. 453 & 893 (1912).
[19]E. Rutherford,Phil. Mag. xxiv. pp. 453 & 893 (1912).
[20]Loc. cit.
[20]Loc. cit.
[21]Loc. cit.
[21]Loc. cit.
[22]Communicated by the Author.
[22]Communicated by the Author.