A spectroscopic instrument is capable of resolving two closely spaced wavelengths, and + , provided that the ratio / is smaller than 8000 . This instrument is employed to examine the spectral lines of the Balmer series of hydrogen. Approximately how many lines can the instrument resolve?

Step-by-step solution

The wavelength of the lines in the Balmer series is given by the Rydberg formula: 1 = R_H ( 1 2^2 - 1 n^2 ) where n = 3, 4, 5, Differentiating both sides with respect to n , we get the wavelength difference between adjacent lines for n = 1 : ^2 = R_H 2 n^3 = 2 R_H ^2 n^3 The resolving power of the instrument is given by: = n^3 2 R_H From the Rydberg formula, for large n , we can approximate: 1 R_H 4 R_H 4 Substituting this into the resolving power expression: n^3 2 4 = n^3 8 Given that the instrument can resolve li