Final answer:
The Doppler broadening of the Hα line in a star with a temperature of 20,000 K cannot be determined from the temperature alone; other factors such as the star's mass and atmospheric composition are also relevant.
Step-by-step explanation:
The question asks how large the Doppler broadening of the Hα line is in a star whose temperature is 20,000 K. The Doppler broadening of spectral lines is caused by the thermal motion of particles that emit or absorb light. In the context of a star, this thermal motion is due to the star's temperature. One of the main factors that influence the broadening of a spectral line is indeed the temperature of the emitting or absorbing material, as higher temperatures lead to higher velocities of particles. Consequently, this results in a greater spread in the velocities and a corresponding Doppler broadening of the spectral lines.
Answer choice D, 'Cannot be determined from the given information', is correct because the precise amount of Doppler broadening of the Hα line cannot be determined solely from the temperature of the star, without additional information such as the mass and composition of the star's atmosphere.