In general, the narrower the spectral line of a star

A.the hotter the star is
B.the bigger the star is
C.the denser the star is
D.the smaller that star is
E.the cooler the star is

E. the cooler the star is .
Lower temperatures result less Doppler broadening of lines in the stellar atmosphere.

Therefore, cooler stars typically have narrower spectral lines.

In general, the narrower the spectral line of a star, the cooler the star is. Lower temperatures result in less Doppler broadening of lines in the stellar atmosphere.

To understand why the answer is E, let's break down the options and explain why they are incorrect:

A. The hotter the star is: A hot star would actually have broader spectral lines. When a star is hotter, the atoms in its atmosphere are more agitated and moving at higher speeds, causing Doppler broadening of the spectral lines. This results in a wider and less distinct line.

B. The bigger the star is: The size of the star does not have a direct correlation with the width of its spectral lines. The width of the lines is mainly determined by the properties of the star's atmosphere, such as temperature and density.

C. The denser the star is: While the density of a star's atmosphere can affect the width of the spectral lines, it is not the primary factor. Density alone does not determine the width of the lines; other factors, such as temperature, have a more significant influence.

D. The smaller the star is: The size of the star does not directly affect the width of its spectral lines. The width of the lines primarily depends on the properties of the star's atmosphere, such as temperature and density.

E. The cooler the star is: This is the correct answer. When a star is cooler, the atoms in its atmosphere are moving at lower speeds, resulting in less Doppler broadening of the spectral lines. As a result, the lines appear narrower and more distinct.

Overall, the width of a star's spectral lines is primarily influenced by its temperature, with cooler stars displaying narrower lines compared to hotter stars.