Question

(17%) Problem is Passing an electric cu ent through an unknown gas produces several distinct wavelengths of visible light. In this problem you will find the wavelengths of the unknown spectrum by observing that they form first-order maxima at angles of 24.1 30.5",36, and 41.6 when projected on a diffraction grating having 10,000 lines per centimeter. Randomized Variables 2-30.5 # 36" θ4 . 416" 25% Part (a) 25% Part (b) 25% Part (c) What is the wavelength (in nm) for the line at 367 25% Partid) whatísthewavelength.(innm) for the line at 416.2 what is the wavelength (in nm) for the line at 24.r? what is the wavelength (in nm) for the line at 305"? i- Grade Sumn Deductions

Parts a through d please.

Answer 1

We know that

d sin(theta) = m lambda

m = 1

lambda = d sin(theta)

d = 10,000 per cm = 10,00000 lines per m

d = 1/1000000 = 10^-6 m

a)lambda1 = 10^-6 x sin24.1 = 408.33 x 10^-9 m

Hence, lambda1 = 408.33 nm

b)lambda2 = 10^-6 x sin30.5 = 507.54 x 10^-9 m

lambda2 = 507.54 nm

c)lambda3 = 10^-6 x sin36 = 587.79 x 10^-9 m

lambda2 = 587.79 nm

d)lambda4 = 10^-6 x sin41.6 = 663.93 x 10^-9 m

lambda2 = 663.93 nm