EBK LOOSE-LEAF VERSION OF UNIVERSE
EBK LOOSE-LEAF VERSION OF UNIVERSE
11th Edition
ISBN: 9781319227975
Author: KAUFMANN
Publisher: VST
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Chapter 8, Problem 20Q

(a)

To determine

The diameter of the disk as shown in the figure below using the scale bar provided below it.

EBK LOOSE-LEAF VERSION OF UNIVERSE, Chapter 8, Problem 20Q

(a)

Expert Solution
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Answer to Problem 20Q

Solution:

The diameter is, approximately, 560 au.

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 560 au.

Conclusion:

Hence, the diameter of the disk is 560 au , approximately.

(b)

To determine

The volume of the disk if its thickness is 50 au.

(b)

Expert Solution
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Answer to Problem 20Q

Solution:

Volume of the disk is 4.15×1040 m3.

Explanation of Solution

Given data:

The thickness of the disk is 50 au and diameter obtained above is 560 au.

Formula used:

The expression for volume of the disk is written as,

V=πr2t

Here, V, r and t are the volume, radius and thickness, respectively.

Use the conversion formula, 1 au3=3.348×1033 m3.

Explanation:

The expression for the radius of the disk (r) is written as,

r=d2

Here, d is the diameter of disk.

Substitute 560 au for d.

r=560 au2=280 au

Recall the expression for the volume of the disk.

V=πr2t

Substitute 280 au for r and 50 au for t.

V=π×(280 au)2×50 au=(1.23×1040 au3)(3.348×1033 m31 au3)=4.15×1040 m3

Conclusion:

Thus, the volume of the disk is 4.15×1040 m3.

(c)

To determine

The number of hydrogen atoms and hydrogen atoms per cubic meter of the disk if the total mass of the disk is 2×1028 kg and the mass of a single hydrogen atom is 1.673×1027 kg.

(c)

Expert Solution
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Answer to Problem 20Q

Solution:

The total number of hydrogen atoms in the disk is 1.19×1055 

Explanation of Solution

Given data:

The thickness of the disk is 50 au and its total mass is 2×1028 kg. It is composed only of hydrogen. Mass of a single hydrogen atom is 1.673×1027 kg.

Formula used:

The expression for the total number of hydrogen atoms (N) is written as,

N=Mm

Here, M and m are the masses of the disk and the hydrogen atom, respectively.

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:

N=Mm

Substitute 2×1028 for M and 1.673×1027 for m.

N=2×1028 kg1.673×1027 kg=1.19×1055

Conclusion:

Thus, the total number of hydrogen atoms in the entire disk is 1.19×1055.

(d)

To determine

The number of hydrogen atoms per cubic meter of the disk. Also compare it with the density of air, which contains about 5.4×1025 atoms per cubic meter.

(d)

Expert Solution
Check Mark

Answer to Problem 20Q

Solution:

Number of hydrogen atoms per cubic meter is 1.28×1014.

Explanation of Solution

Given data:

The thickness of the disk is 50 au, total mass is 2×1028 kg and it is composed only of hydrogen. Mass of a single hydrogen atom is 1.673×1027 kg. Air contains about 5.4×1025 atoms per cubic meter.

Formula used:

The number of atoms per cubic meter (n) is written as,

n=NV

Here, V is volume of the disk and N is total number of hydrogen atoms in the disk.

Explanation:

From part (c), total number of hydrogen atoms in the disk (N) is 1.19×1055 .

From part (b), volume of the disk is 4.15×1040 m3.

Recall the expression for number of atoms per cubic meter (n).

n=NV

Substitute 1.19×1055  for Nand 4.15×1040 m3 for V.

n=1.19×1055 atoms 4.15×1040 m3=2.9×1014 atomsm3

Thus, the disk has a density much less than that of the air we breathe, which is 5.4×1025 atoms per cubic meter.

Conclusion:

Thus, the number of hydrogen atoms per cubic meter is 2.9×1014.

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