5. (15pts) Previously, we saw that spectral lines have a natural broadening due

Question

5. (15pts) Previously, we saw that spectral lines have a natural broadening due to the quantum mechanical uncertainty in the energy for any particular excited state of the atom. Another type of spectral line broadening manifests itself due to the rotation of the object we're studying. An A0 star with strong hydrogen Balmer lines rotates with a velocity of 200 km/s. Assume that we observe the spectrum of such a star, and our line of sight is perpendicular to the star's axis of rotation Assume also that we cannot resolve the star (i.e., that light from the entire disk of the star we observe is integrated in our spectrum). Use the Doppler effect to determine how much the Ha line is broadened due to stellar rotation. (Hint: Part of the star is moving towards you and part of it is moving away from you.,)

Explanation / Answer

Case(i): When object is moving away:

Wavelength of light when object is moving away = ((C+V)*Wavelength/C); Here, C= velocity of light =3*10^8 m/s; V= velocity of object = 2*10^5 m/s; Wavelength = Wavelength of strong balmer line= 547.236 nm

On substituting all values, we get

=> Wavelength of light when object is moving away =545.415 nm

Case(ii): When object is approaching:

Wavelength of light when object is approaching = ((C-V)*Wavelength/C); Here, C= velocity of light =3*10^8 m/s; V= velocity of object = 2*10^5 m/s; Wavelength = Wavelength of strong balmer line= 546.226 nm

On substituting all values, we get

=> Wavelength of light when object is moving away =54.258 nm

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