A spectroscopic instrument can resolve two nearby wavelengths and… - Vidyadip

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?

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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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