Question

An electric current through neon gas produces several distinct wavelengths of visible light. What are the wavelengths (in nm) of the neon spectrum, if they form first-order maxima at angles of 49.67°, 50.65°, 52.06°, and 52.89° when projected on a diffraction grating having 11,000 lines per centimeter? (Round your answers to the nearest nanometer. Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign. Enter your answers from smallest to largest.)

Answer 1

Step-by-step explanation:

If a be grating element

a = 1 x 10⁻² / 11000

= .0909 x 10⁻⁵

= 909 x 10⁻⁹ m

for first order maxima , the condition is

a sinθ = λ where λ is wavelength

909 x 10⁻⁹ sin 49.67 = λ₁

λ₁ = 692.95 nm .

λ₂ = 909 x 10⁻⁹ sin 50.65

= 702.91 nm

λ₃ = 909 x 10⁻⁹ sin 52.06

= 716.88 nm

λ₄ = 909 x 10⁻⁹ sin 52.89

= 724.90 nm

692.95 nm , 702.91 nm , 716.88 nm , 724.90 nm .