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College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

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BuyFindarrow_forward

College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
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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