Question

A student used a diffraction grating with 633 lines/mm to determine an unknown wavelength of light. The light passed through the grating, and the pattern was observed on a paper placed 90.0 cm past the grating. The distance from the center bright spot to the second bright spot from the center was measured to be 71.9 cm. What was the wavelength of light in nanometers (nm)? (State answer in nanometers as a whole number with no digits right of decimal.)

Answer 1

Answer:

Given, a diffraction grating with 633 lines/mm, so d = 1/633 mm = (1/633) x 10-3 m = 1.57 x 10-6 m distance between the grating and the paper is D = 90 cm = 0.90 m, distance between the center bright spot and the second bright spot is h = 71.9 cm = 0.719 m

Using the diffraction expression for grating is d sin = n

Here, n = 2. So tan = h/D or = tan-1(h/D) = tan-1 (0.719/0.90) = 38.580

Therefore, the wavelength used for the experiment is

= d sin / n = (1.57 x 10-6 m) sin38.580 / 2

    = (1.57 x 10-6 m) (0.6236) /2

    = 0.489 x 10-6 m

     = 489 x 10-9 m

   Hence, = 489 nm