Q61. Recent findings in astrophysics ... [FREE SOLUTION]

Chapter 1: Q61. (page 20)

Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius $R = 13.7 脳 10^{9} light years = 13.0 脳 10^{25} m$ with an average total mass density of about $1 脳 10^{- 26} kg / m^{3}$ . Only about 4% of total mass is due to 鈥渙rdinary鈥� matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light- year, see the Problem19.)

Short Answer

Expert verified

There is approximately $4 脳 10^{51} kg$ of ordinary mass in the observable universe.

Step by step solution

Step 1. Definition of density

Density is a physical quantity that establishes a relationship between the mass and volume of an object. It is given by the ratio of the mass per unit volume.

Step 2. Identification of the given data

Radius of the modeled sphere, $R = 13.7 脳 10^{9} light years = 13 脳 10^{25} m$

Mass density of the sphere, $蚁 = 1 脳 10^{- 26} kg / m^{3}$

Step 3. Determination of the volume of the observable universe

The universe is modeled into a sphere whose volume is:

$\begin{matrix} V = \frac{4}{3} 蟺 R^{3} \\ = \frac{4}{3} 脳 \frac{22}{7} 脳 {(13 脳 10^{25} m)}^{3} \\ = 9.20 脳 10^{78} m^{3} \end{matrix}$

Step 4. Determination of the total mass of the sphere from density

The formula of density is:

$\begin{matrix} 蚁 = \frac{m}{V} \\ m = 蚁 V \end{matrix}$

Substituting the known numerical values,

$\begin{matrix} m = (1 脳 10^{- 26} kg / m^{3}) (9.20 脳 10^{78} m^{3}) \\ = 9.20 脳 10^{52} kg \end{matrix}$

Step 5. Determination of ordinary matter/mass

Ordinary matter is only 4% of the total mass. So, the ordinary mass is:

$\begin{matrix} m' = 4 % o f m \\ = \frac{4}{100} 脳 9.20 脳 10^{- 52} kg \\ = 3.68 脳 10^{51} kg \\ 鈮� 4 脳 10^{51} kg \end{matrix}$

Thus, there is about $4 脳 10^{51} kg$ of ordinary mass in the observable universe.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Step 1. Definition of density

Step 2. Identification of the given data

Step 3. Determination of the volume of the observable universe

Step 4. Determination of the total mass of the sphere from density

Step 5. Determination of ordinary matter/mass

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Engineering Physics

Solid State Physics

Quantum Physics

Geometrical and Physical Optics

Torque and Rotational Motion

Study anywhere. Anytime. Across all devices.