To what series does the spectral line of atomic hydrogen belong if its wave number is equal to the difference between the wave numbers of the following two lines of the Balmer series: `486.1`and `410.2nm`? What is the wavelength of that time?

Explanation

The Balmer line of wavelength `486.1nm` is due to the transition `4rarr2` while the Balmer line of wavelength 410.2nm is due to the transition `6rarr2`. The line whose wave number corresponds to the difference in wave numbers of these two lines is due to the transition `6rarr4`. That line belongs to the Brackett series. The wavelength of this line is
`(1)/((1)/(lambda_(2))-(1)/(lambda_(1)))=(lambda_(1)lambda_(2))/(lambda_(1)-lambda_(2))=2.627mu m`.