A spectroscopic instrument can resolve two nearby wavelengths λ and λ + Δλ if λ/Δλ 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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Solution

The range of wavelength falling in Balmer series is between 656.3 nm and 365 nm.
It is given that the resolution of the instrument is λ/ (λ + ∆λ) < 8000.

Number of wavelengths in this range will be calculated in the following way:
$\frac{656.3 - 365}{8000} = 36$
Two lines will be extra for the first and last wavelength.
∴ Total number of lines = 36 + 2 = 38

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