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Chapter 13: Problem 10

Star A is more massive than star B. Both are main-sequence stars. Therefore, star A is than star B. (Choose all that apply.) a. brighter b. fainter c. hotter d. colder e. larger f. smaller

Short Answer

Expert verified
Star A is brighter, hotter, and larger than star B.

Step by step solution

01

- Understand Main-Sequence Characteristics

Both stars A and B are main-sequence stars. Main-sequence stars generate energy through nuclear fusion, converting hydrogen into helium in their cores.
02

- Mass and Luminosity Relationship

The greater the mass of a main-sequence star, the higher its luminosity. Therefore, star A, being more massive than star B, is brighter. This means option a (brighter) is correct.
03

- Mass and Temperature Relationship

More massive main-sequence stars are also hotter because they have higher core temperatures to support the fusion of hydrogen. This makes star A hotter than star B. Hence, option c (hotter) is correct.
04

- Mass and Size Relationship

More massive main-sequence stars are larger in size compared to less massive ones. Therefore, star A, which is more massive, will be larger than star B. So, option e (larger) is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mass and Luminosity Relationship
In main-sequence stars, there's a clear relationship between mass and luminosity. The more massive a star is, the brighter it shines. This happens because the larger mass fuels more nuclear reactions in the star's core.

These reactions release significant amounts of energy, increasing the star's luminosity. For example:
  • A star with twice the mass of our Sun can be up to ten times more luminous.
Hence, if star A has a greater mass than star B, star A will also be brighter. This relationship helps astronomers determine stellar properties by observing their brightness.
Mass and Temperature Relationship
Another crucial characteristic of main-sequence stars is the relationship between mass and temperature. The core of a more massive star generates more pressure, leading to higher temperatures needed for hydrogen fusion.

This increased temperature not only drives nuclear reactions more quickly but also raises the star’s surface temperature.

For instance:
  • A star with significantly higher mass than our Sun may have surface temperatures reaching up to 30,000 K.
Thus, with star A being more massive than star B, it is also hotter. This is why more massive stars often appear blue or white, denoting higher temperatures.
Mass and Size Relationship
Lastly, the mass and size of main-sequence stars are directly related. A star's size typically increases with its mass. The gravitational pressure in more massive stars results in larger volumes.

This expanded size helps maintain equilibrium within the star.
  • If star A has a higher mass than star B, it will naturally be larger in diameter.
Such larger stars also exhibit different stages and lifecycles compared to smaller stars, affecting how they evolve and end their lives.

Hence, a more massive star A will indeed be larger compared to a less massive star B, impacting not just their appearance but also their life span and evolutionary path.

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Most popular questions from this chapter

O stars have relatively featureless visible spectra because 0 stars are a. too hot to have atoms. b. so hot that most atoms are ionized. c. not hot enough for atoms to be ionized. d. so cool that must atoms are in the ground state.

The light from stars passes through dust in the Milky Way Galaxy before it reaches Earth, making stars appear dimmer than they actually are. How does this phenomenon affect stellar trigonometric parallax? How does it affect spectroscopic parallax?

Star A and star B are two blue stars at nearly the same distance from Earth. Star A is many times brighter than star B. Which of the following statements is true? a. Star A is a main-sequence star, and star B is a red giant. b. Star A is a main-sequence star, and star \(\mathrm{B}\) is a blue giant. c. Star A is a white dwarf, and star B is a blue giant. d. Star A is a blue giant, and star B is a white dwarf.

Find the peak wavelength of blackbody emission for a star with a temperature of about \(10,000 \mathrm{K}\). In what region of the spectrum does this wavelength fall? What color is this star?

To know certain properties of a star, you must first determine the star's distance. For other properties, knowledge of distance is not necessary. Into which of these two categories would you place each of the following properties: size, mass, temperature, color, spectral type, and chemical composition? In each case, state your reason(s).
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