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Chapter 1: Problem 27

The Sun's mass is \(1.99 \times 10^{30} \mathrm{~kg}\), three-quarters of which is hydrogen. The mass of a hydrogen atom is \(1.67 \times 10^{-27} \mathrm{~kg}\). How many hydrogen atoms does the Sun contain? Use powers-of-ten notation.

Short Answer

Expert verified
The Sun contains approximately \(8.94 \times 10^{57}\) hydrogen atoms.

Step by step solution

01

Calculate the mass of hydrogen in the Sun

Since the sun consists of 75% hydrogen, we calculate the mass of hydrogen in the sun: \( mass_{H_{sun}} = 0.75 \times 1.99 \times 10^{30} \mathrm{~kg} \).
02

Calculate the number of hydrogen atoms

Now, to find out the number of hydrogen atoms, the mass of hydrogen in the sun needs to be divided by the mass of a single hydrogen atom, which gives \( N_{H_{atoms}} = \frac{mass_{H_{sun}}}{mass_{H_{atom}}} = \frac{0.75 \times 1.99 \times 10^{30} \mathrm{~kg}}{1.67 \times 10^{-27}\mathrm{~kg}}\).
03

Simplify the result

When calculated, the division result from Step 2 will not be exactly an integer but a decimal number. However, because the amounts this big can't be represented in full precision, it is sufficient to calculate to the closest power of ten.

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Most popular questions from this chapter

50\. Use the Starry Night Enthusiast \({ }^{\mathrm{TM}}\) program to investigate the Milky Way Galaxy. Select Deep Space \(>\) Local Universe in the Favourites menu. Click and hold the minus (-) symbol in the Zoom control on the toolbar to adjust the field of view to an appropriate value for this image of the Milky Way. A foreground image of astronaut's feet may be superimposed upon this view. Click on View > Feet to remove this foreground, if desired. The view shows the Milky Way near the center of the window against a background of distant galaxies as seen from a point in space 282,000 light- years from the Sun. To center the Milky Way in the view, position the mouse cursor over the Milky Way and click and hold the mouse button (on a two-button mouse, click the right button). Select Centre from the drop down menu that appears. (a) To view the Milky Way from different angles, hold down the SHIFT key on the keyboard. The cursor should turn into a small square surrounded by four small triangles. Then hold down the mouse button (the left button on a two-button mouse) and drag the mouse in order to change the viewing angle. This will be equivalent to your moving around the galaxy, viewing it against different backgrounds of both near and far galaxies. How would you describe the shape of the Milky Way? (b) You can zoom in and zoom out on this galaxy using the Zoom buttons at the right side of the toolbar. (c) Another way to zoom in on the view is to change the elevation of the viewing location. Click the Find tab at the left of the view window and double-click the entry for the Sun. This will center the view on the Sun. Now use the elevation buttons to the left of the Home button in the toolbar to move closer to the Sun. Move in until you can see the planets in their orbits around the Sun, then zoom back out until you can see the entire Milky Way Galaxy again. Are the Sun and planets located at the center of the Milky Way? How would you describe their location?

Angular measure describes how far apart two objects appear to an observer. From where you are currently sitting, estimate the angular distance between the floor and the ceiling at the front of the room you are sitting in, the angular distance between the two people sitting closest to you, and the angular size of a clock or an exit sign on the wall. Draw sketches to illustrate each answer and describe how each of your answers would change if you were standing in the very center of the room.

A person with good vision can see details that subtend an angle of as small as 1 arcminute. If two dark lines on an eye chart are 2 millimeters apart, how far can such a person be from the chart and still be able to tell that there are two distinct lines? Give your answer in meters.

A hydrogen atom has a radius of about \(5 \times 10^{-9} \mathrm{~cm}\). The radius of the observable universe is about 14 billion light-years. How many times larger than a hydrogen atom is the observable universe? Use powers-of- ten notation.

What are degrees, arcminutes, and arcseconds used for? What are the relationships among these units of measure?
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