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The D line in the spectrum of sodium is a doublet with wavelengths 589.0and589.6nm. Calculate the minimum number of lines needed in a grating that will resolve this doublet in the second-order spectrum.

Short Answer

Expert verified

The minimum number of lines needed in the grating, to resolve the douplet, is 491.

Step by step solution

01

The resolving power

It is known the resolving power of a grating is given by-

R=Nm=λavg∆λ

where Nis the number of rulings in the grating and mis the order of the linesλavg, is the average of wavelengths, and ∆λis the wavelength difference.
02

Given Data

The wavelength of the sodium doublet is - 589.0nmand589.6nm

03

The number of rulings

The resolving power of the grating is given as-

Nm=λavgΔλ

From the given values in the question, we have

N×2=589.0nm+589.6nm2589.6nm-589.0nmN×2=1178.6nm20.6nm

On solving further,

N=1178.6nm0.6nm×2×2N=491

Thus, the minimum number of lines needed in the grating is 491.

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