Question

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

a) 590.6 nm, 594.2 nm
b) 589.0 nm, 590.5 nm
c) 588.5 nm, 592.0 nm
d) 587.8 nm, 591.3 nm

Answer 1

To find the wavelengths to an accuracy of 0.1 nm, we can use the formula for diffraction using a grating. We have two first-order maxima at angles of 36.093º and 36.129º. Solving the equations will give us the two wavelengths: 589.0 nm, 590.5 nm.

Step-by-step explanation:

To find the wavelengths to an accuracy of 0.1 nm, we can use the formula for diffraction using a grating:

msinθ = mλ/d

Where m is the order of the maxima, θ is the angle at which the maxima occurs, λ is the wavelength, and d is the spacing between the lines on the grating.

We have two first-order maxima at angles of 36.093º and 36.129º. Plugging in the values, we get:

sin(36.093º) = λ₁ / (100,000 nm/cm)

sin(36.129º) = λ₂ / (100,000 nm/cm)

Solving these equations will give us the two wavelengths.

The correct answer is 589.0 nm, 590.5 nm.