   Chapter 27, Problem 26PE

Chapter
Section
Textbook Problem

An electric current through hydrogen gas produces several distinct wavelengths of visible light. What are the wavelengths of the hydrogen spectrum, if they form first-order maxima at angles of 24.2°, 25.7°, 29.1°, and 41.0° when projected on a diffraction grating having 10,000 lines per centimeter? Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics

To determine

The wavelengths of the hydrogen spectrum.

Explanation

Given info:

N=10000linescmθ1=24.20θ2=25.70θ3=29.10θ4=41.00m=1

Formula used:

There is constructive interference for a diffraction grating when,

dsinθ=mλ,   m=0,1,1,2,2....

Calculation:

First let us find slit separation,

N=10000linescmd=1× 10 210000=1000nm

θ1=24.20

dsinθ=mλλ1=1000×sin24

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