Question
A spectroscopic instrument can resolve two nearby wavelengths $\lambda$ and $\lambda+\Delta\lambda$ if $\frac{\lambda}{\Delta\lambda}$ is smaller than 8000. This is used to study the spectral lines of the Balmer series of hydrogen. Approximately how many lines will be resolved by the instrument?

Answer

The range of Balmer series is 656.3nm to 365nm. It can resolve $\lambda$ and $\lambda+\Delta\lambda$ if $\frac{\lambda}{\Delta\lambda}=8000$

$\therefore$ No. of wavelength in the range $=\frac{656.3-365}{8000}=36$

Total no. of lines 36 + 2 = 38 [extra two is for first and last wavelength]

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