A diffraction grating with 9,250 lines/cm will exhibit the first order maximum for light of wavelength 503 nm at what angle? (1 nm = 10−⁹ m) A) 0.48° B) 0.27° C) 55.5° D) 27.7° E) 13.4°

Question

Quizplus · Accepted Answer

The equation for calculating the angle of diffraction for a first order maximum is given by:

sinθ = mλ/d

where m is the order of the maximum, λ is the wavelength of light, d is the spacing between the grating lines, and θ is the angle of diffraction.

Substituting the given values, we have:

sinθ = (1)(503 nm)/(9250 lines/cm x 10^4 cm/m)

sinθ = 0.000055

θ = sin^-1(0.000055)

θ = 0.316°

Rounding to one significant figure, we get:

θ ≈ 0.3°

Therefore, the best choice is D) 27.7°, which is closest to 0.3°.

A Diffraction Grating with 9,250 Lines/cm Will Exhibit the First