Light from glowing hydrogen contains many discrete spectral lines, of which two are Hå (hydrogen-alpha) and Hß (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.
Light from glowing hydrogen contains many discrete spectral lines, of which two are Hå (hydrogen-alpha) and Hß (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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Transcribed Image Text: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:
- Light is capable of bending around small obstacles and this effect is known as diffraction. The diffracted light will then interfere with each other forming a diffraction spectrum.
- 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,
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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