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Get Full Access to College Physics - 1 Edition - Chapter 11 - Problem 10pe
Get Full Access to College Physics - 1 Edition - Chapter 11 - Problem 10pe

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# Solved: There is relatively little empty space between

ISBN: 9781938168000 42

## Solution for problem 10PE Chapter 11

College Physics | 1st Edition

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College Physics | 1st Edition

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Problem 10PE

There is relatively little empty space between atoms in solids and liquids, so that the average density of an atom is about the same as matter on a macroscopic scale—approximately 103 kg/m3 . The nucleus of an atom has a radius about 10−5 that of the atom and contains nearly all the mass of the entire atom. (a) What is the approximate density of a nucleus? (b) One remnant of a supernova, called a neutron star, can have the density of a nucleus. What would be the radius of a neutron star with a mass 10 times that of our Sun (the radius of the Sun is 7×108 m )?

Step-by-Step Solution:

Part (a)

Step 1 of 7:

The atoms in solids and liquids contain void space. There is no matter inside the atom except the atomic particles. Hence the average density on the macroscopic scale remains same. The approximate atomic density is provided. Most of the mass of the atom is concentrated in the nucleus. The radius of the nucleus is about 10-5 times than that of the atom. We are going to calculate the density of the nucleus.

The mass of the nucleus = the mass of the atom

Step 2 of 7:

The density of the nucleus is expressed as

Considering the nucleus as perfect sphere, the volume is given as

Therefore the density is rewritten as

Solving for mass of nucleus

Step 3 of 7:

The density of the atom is expressed as

the volume is given as

Therefore the density is rewritten as

Solving for mass of atom

Step 4 of 7:

Since the mass of the nucleus is almost equal to the mass of the atom, we can compare the equations (2) and (4). Therefore

Substituting the value of the radius of the nucleus, the density of the atom and dividing the common terms, we get

Hence the density of the nucleus is 1018 kg/m3.

Part (b)

Step 5 of 7

Step 6 of 7