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2) Light from glowing hydrogen contains many discrete spectral lines, of which two are Ha (hydrogen-alpha) and HE (hydrogen-beta), with wavelengths of 656.3 nm and 486.1 nm, respectively. Find the first-order angular separation between these wavelengths in a spectrometer that uses a grating with 6000 slits per cm. (

2) Light from glowing hydrogen contains many discrete spectral lines, of which two are Ha (hydrogen-alpha) and HE (hydrogen-beta), with wavelengths of 656.3 nm and 486.1 nm, respectively. Find the first-order angular separation between these wavelengths in a spectrometer that uses a grating with 6000 slits per cm. (

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2) Light from glowing hydrogen contains many discrete spectral lines, of which two are Ha (hydrogen-alpha) and HB (hydrogen-beta), with wavelengths of 656.3 nm and 486.1 nm, respectively. Find the first-order angular separation between these wavelengths in a spectrometer that uses a grating with 6000 slits per cm.
Transcribed Image Text:2) Light from glowing hydrogen contains many discrete spectral lines, of which two are Ha (hydrogen-alpha) and HB (hydrogen-beta), with wavelengths of 656.3 nm and 486.1 nm, respectively. Find the first-order angular separation between these wavelengths in a spectrometer that uses a grating with 6000 slits per cm.
Expert Solution
Concept and Principle:
  • Diffraction grating creates a diffraction spectrum. It is formed by the diffracted waves interfering with each other.

 

  • A diffraction spectrum consists of points of high and low intensity. Maximum intensity happens due to constructive interference and minimum due to destructive interference.

 

  • The condition for constructive interference is given by,

dsinθ=mλ

Here d is the slit width, θ is the angular position, m is the order of the fringe, and λ is the wavelength.

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