Passing an clcctric current through an unknown gas produces several distinct wav

Question

Passing an clcctric current 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 23.5degree, 30.1degree, 34.3degree and 41.2degree when projcctcd on a diffraction grating having 10,000 lines per centimeter. What is the wavelength (in nm) for the line at 23.5degree? What is the wavelength (in nm) for the line at 30.1degree? What is the wavelength (in nm) for the line at 34 3degree? What is the wavelength (in nm) for the line at 41.2degree?

Explanation / Answer

here,

number of slits , n = 10000 lenes per cm

slit width , d = 1/n = 10^-6 m

a)

theta = 23.5 degree

let the wavelength be lamda

d * sin(theta) = n * lamda

for first order , n =1

10^-6 * sin(23.5) = 1 * lamda

lamda = 3.99 * 10^-7 m = 399 nm

b)

theta = 30.1 degree

let the wavelength be lamda

d * sin(theta) = n * lamda

for first order , n =1

10^-6 * sin(30.1) = 1 * lamda

lamda = 5.02 * 10^-7 m = 501.5 nm

c)

theta = 34.3 degree

let the wavelength be lamda

d * sin(theta) = n * lamda

for first order , n =1

10^-6 * sin(34.3) = 1 * lamda

lamda = 5.64 * 10^-7 m = 563.5 nm

d)

theta = 41.2 degree

let the wavelength be lamda

d * sin(theta) = n * lamda

for first order , n =1

10^-6 * sin(41.2) = 1 * lamda

lamda = 6.59 * 10^-7 m = 658.7 nm

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