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allsm [11]
3 years ago
5

A diffraction grating with 161 slits per centimeter is used to measure the wavelengths emitted by hydrogen gas. At what angles i

n the first-order spectrum would you expect to find the two violet lines of wavelength 434 nm and of wavelength 410 nm
Physics
1 answer:
Tresset [83]3 years ago
4 0

Answer:

\theta_1  = 0.400^o

\theta_2   =0.378^o

Explanation:

From the question we are told that

    The  number of slits per cm is  k =  161\  slits\  per\  cm =  161 \  slits\  per\  0.01 m

    The order of the maxima is  n =  1

    The wavelength are  \lambda_1 = 434 nm  =  434 *10^{-9} \ m \ \ \ , \lambda_2 = 410nm =  410 *10^{-9} \  m

The  spacing between the slit is mathematically represented as

           d =  \frac{ 0.01}{k}

=>       d =  \frac{ 0.01}{161}

=>         d = 6.211 *10^{-5} \ m

Generally the condition for constructive interference is  

        n\lambda  =  d \ sin \theta

At  \lambda_1

      \theta _1  =  sin^{-1} [ \frac{1  *  434 *10^{-9}}{6.211 *10^{-5}} ]

      \theta_1  = 0.400^o

At  \lambda_2

       \theta _2  =  sin^{-1} [ \frac{1  *  410 *10^{-9}}{6.211 *10^{-5}} ]

       \theta_2   =0.378^o

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