Question

The yellow light from a sodium vapor lamp seems to be of pure wavelength, but it produces two first-order maxima at 36.093° and 36.129° when projected on a 10,000 line per centimeter diffraction grating. What are the two wavelengths to an accuracy of 0.1 nm?

Answer 1

The wavelengths of the yellow light from a sodium vapor lamp diffracted on a 10,000 line per centimeter diffraction grating are 589.6 nm and 590.5 nm.

Step-by-step explanation:

The yellow light from a sodium vapor lamp is diffracted when projected on a 10,000 line per centimeter diffraction grating, producing two first-order maxima at angles of 36.093° and 36.129°.

To find the two wavelengths to an accuracy of 0.1 nm, we can use the formula for the grating equation: nλ = d sin(θ), where n is the order of the maximum, λ is the wavelength, d is the distance between the lines on the grating, and θ is the angle of diffraction. Rearranging the formula, we get λ = (d/n) sin(θ).

Using n = 1, d = 10,000 lines/cm = 100 lines/mm = 0.01 lines/µm = 0.00001 lines/nm, and θ = 36.093° and 36.129°, we can calculate the wavelengths as follows:

1. λ₁ = (0.00001 lines/nm / 1) sin(36.093°) = 589.6 nm
2. λ₂ = (0.00001 lines/nm / 1) sin(36.129°) = 590.5 nm