A miniature spectrometer used for chemical analysis has a diffraction grating wi

Question

A miniature spectrometer used for chemical analysis has a diffraction grating with800 slits/mm set 25.0 mm in front of the detector "screen." The detector can barely distinguish two bright lines that are 30 m apart in the first-order spectrum.

What is the resolution of the spectrometer at a wavelengthof 450 nm ? That is, if two distinct wavelengths can barely be distinguished, one of them being 450 nm , what is the wavelength difference between the two?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

The resolving Power of a spectromter

R = delta L/L = mN

R = 800slits/mm * 1000/1 mm

R = 8 e 5

diff in wavelength = mN L

dL = 8 e 5 * 5 e-9

dL = 40 cm

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