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(a)
The diameter of the disk as shown in the figure below using the scale bar provided below it.
(a)
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Answer to Problem 20Q
Solution:
The diameter is, approximately,
Explanation of Solution
This can be calculated directly by calibrating our usual scale with the scale bar provided below the figure and measuring the diameter of the disk. This diameter comes to be around
Conclusion:
Hence, the diameter of the disk is
(b)
The volume of the disk if its thickness is
(b)
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Answer to Problem 20Q
Solution:
Volume of the disk is
Explanation of Solution
Given data:
The thickness of the disk is
Formula used:
The expression for volume of the disk is written as,
Here,
Use the conversion formula,
Explanation:
The expression for the radius of the disk (r) is written as,
Here, d is the diameter of disk.
Substitute
Recall the expression for the volume of the disk.
Substitute
Conclusion:
Thus, the volume of the disk is
(c)
The number of hydrogen atoms and hydrogen atoms per cubic meter of the disk if the total mass of the disk is
(c)
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Answer to Problem 20Q
Solution:
The total number of hydrogen atoms in the disk is
Explanation of Solution
Given data:
The thickness of the disk is
Formula used:
The expression for the total number of hydrogen atoms
Here,
Explanation:
If the total mass of the disk and the mass of each hydrogen atom are given, provided that the disk is composed entirely of hydrogen atoms, the number of hydrogen atoms is:
Substitute
Conclusion:
Thus, the total number of hydrogen atoms in the entire disk is
(d)
The number of hydrogen atoms per cubic meter of the disk. Also compare it with the density of air, which contains about
(d)
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Answer to Problem 20Q
Solution:
Number of hydrogen atoms per cubic meter is
Explanation of Solution
Given data:
The thickness of the disk is
Formula used:
The number of atoms per cubic meter
Here,
Explanation:
From part (c), total number of hydrogen atoms in the disk (N) is
From part (b), volume of the disk is
Recall the expression for number of atoms per cubic meter
Substitute
Thus, the disk has a density much less than that of the air we breathe, which is
Conclusion:
Thus, the number of hydrogen atoms per cubic meter is
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Chapter 8 Solutions
Universe
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