The grading has 525 lines/mm. The distance D = 285 mm. A light source (not a las

Question

The grading has 525 lines/mm. The distance D = 285 mm. A light source (not a laser) produces a first-order (m = 1) spectral line located at x1 = 75.3 mm.

What is the wavelength ?of this line? (Units required.)

What is its photon energy Ein eV?

In a spectroscopy experiment, a diffraction grating is set-up, similar to what is shown below. (Note: the color of the light shown in the diagram is arbitrary.) The grading has 525 lines/mm. The distance D = 285 mm. A light source (not a laser) produces a first-order (m = 1) spectral line located at x1 = 75.3 mm. What is the wavelength ?of this line? (Units required.) What is its photon energy Ein eV?

Explanation / Answer

d*sin(theta)=n*l, here d=grating constant=1/N=1/525

here theta=arctan(75.3/285)=14.8

and n=1, now l=wavelength=?

here calculating, l=4.86*10^-4 mm= 4.86*10^-7 m

photon energy= h*c/l=6.63*10^-34*3*10^8/4.86*10^-7= 4.0878*10^-22 J= 2.55*10^-3 eV

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