M09 - M10 Emission spectrum and electron structure

Every chemical element has a unique emission spectrum which is determined by its electronic structure. Every line in the spectrum is caused by an electron transfer; an electron transition from a higher energy level or excited state to a lower energy level. The excess energy (the difference between the two levels) is released as a photon of light of a specific frequency, which is seen as a line on the spectrum.

In 1885 the Swiss physicist, Balmer, succeeded in describing the visible line spectrum of hydrogen as a function of the wavelength, :

where is the Rydberg constant. By giving n the values 3, 4, 5, 6, ….. , the wavelength of every spectral line is described. The integer n is called the principle quantum number.

The table below gives the calculated and experimental values for the Balmer-line wavelengths (for H) using

= 109677.6 cm^-1.

The infrared and ultraviolet spectral lines of hydrogen can be calculated in a similar way, using the more general formula:

where m and n are both integers, of which n is the larger.

For m=1 the Lyman (ultraviolet) series is obtained. m=2 gives the Balmen (visible) series discussed above and m=3 gives the Paschen (infrared) series.