The three principal visible spectral lines from hydrogen have wavelengths 434 nm

Question

The three principal visible spectral lines from hydrogen have wavelengths 434 nm, 486 nm, and 656 nm. The principal line of sodium is at 589 . A sodium lamp used to calibrate a diffraction grating shows the first-order sodium line at 26.0 degrees from the central maximum.

A). Find the angular position of the first spectral line in hydrogen (434 nm).
B). Find the angular position of the second spectral line in hydrogen (486 nm).
C). Find the angular position of the third spectral line in hydrogen (656 nm).

Explanation / Answer

Given    wave length of sodium line   Na   =   589 nm    A sodium lamp used to calibrate a diffraction grating shows the first-order sodium line at 26.0 degrees from the central maximum           sin Na =    m Na / d                distance between grating lines                d =      m Na     / sin 26                     =   589 nm / sin 26                     =   1.343 m     a)  angular position of the first spectral line in hydrogen    ( 434 nm )               sin 434 = m 434    / d                             =   434 nm / 1.343 m                              =     0.323                   434      = 18.8539 o       b)  angular position of the second spectral line in hydrogen (486 nm                    sin 486 = m 486   / d                             =   486 nm / 1.343 m                              =     0.323                  434     = 21.2154 o        c) angular position of the third spectral line in hydrogen (656 nm               sin 656 = m 656   / d                             =   656 nm / 1.343 m                              =     0.488                  434     = 29.2393o                               =   486 nm / 1.343 m                              =     0.323                  434     = 21.2154 o        c) angular position of the third spectral line in hydrogen (656 nm               sin 656 = m 656   / d                             =   656 nm / 1.343 m                              =     0.488                  434     = 29.2393o                               =   656 nm / 1.343 m                              =     0.488                  434     = 29.2393o  

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