Abstract

How did J.J.Balmer discover the formula of the Balmer series from the spectrum of the hydrogen atom? I don’t know the details of that.

Using numerical calculations written in Julia, we succeeded in deriving the Balmer’s formula from four wavelength data in two methods.

J.J. Balmer conjectured that the four wavelength measurements were equal to simple fractions multiplied by a constant. The first method was to start with the Balmer’s conjecture and find the four fractions that gave the best fit.

The other method was to assume a simple function that the measurements should satisfy and use the method of least squares.

It was possible to show at what stage in the discovery of Balmer’s formula a leap of logic was required.

Keywords

Balmer series; Spectrum of hydrogen atom; Graph of fractional ratio; Method of least squares; Julia program