Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 21, Problem 13Q

(a)

To determine

The density of matter in a neutron and compare it with the average density of a neutron star. It is given that neutron has a mass of 1.7×1027 kg and a radius of about 1015 m.

(a)

Expert Solution
Check Mark

Answer to Problem 13Q

Solution:

The density of neutron is 4.059×1017 kg/m3, which is lesser than the average density of neutron star.

Explanation of Solution

Given data:

The mass of a neutron is 1.7×1027 kg and it has a radius of about 1015 m.

Formula used:

Write the expression for density:

ρ=MV

Here, ρ is the density, M is the mass, and V is the volume.

Write the expression for volume of a sphere:

V=43πr3

Here, V is the volume of a sphere and r is the radius of sphere.

Explanation:

Let’s assume that neutron is a sphere of radius r.

According to question, mass of neutron is 1.7×1027 kg and radius is about 1015 m.

Calculate the volume of a sphere.

Refer to the expression for volume of sphere,

V=43πr3

Substitute 1015 m for r,

V=43π(1015 m)3=4.188×1045 m3

Calculate density of neutron.

Refer to the expression of expression for density of a neutron star,

ρ=MV

Substitute 4.188×1045 m3 for V and 1.7×1027 kg for M:

ρ=(1.7×1027 kg)(4.188×1045 m3)=4.059×1017 kg/m3

Now, compare the density of matter in a neutron with average density of a neutron star.

As average density of neutron in neutron star is 7.3×1017 kg/m3 that is greater than calculated density of neutron.

Conclusion:

Hence, neutron has density of 4.059×1017 kg/m3, which is lesser than the density of a neutron star.

(b)

To determine

Neutrons within a neutron star are overlapping if density of neutron star is more than that of neutron, or are underlapping otherwise. Also, explain whether density at the center of a neutron star is higher than the average density of neutron star. It is given that neutron has mass of 1.7×1027 kg and a radius of about 1015 m.

(b)

Expert Solution
Check Mark

Answer to Problem 13Q

Solution:

As the density of neutron is less than the average density of a neutron star, therefore, neutrons in the neutron star are in overlapping state and density is uniform throughout the neutron star.

Explanation of Solution

Given data:

The mass of neutron is 1.7×1027 kg and radius is about 1015 m.

Introduction:

A neutron star is composed of an incredibly dense sphere of neutrons formed by a supernova explosion. Its average density is about 7.3×1017 kg/m3.

Explanation:

Refer to part (a) of the question, the average density of neutron in a neutron star is 7.3×1017 kg/m3 which is greater than the calculated density of neutron, that is, 4.059×1017 kg/m3.

From the above observation, neutrons in the neutron star are overlapping as density of a neutron is less than the average density of a neutron star.

Also, in a neutron star, density is uniform throughout. In other words, density at the center is same as density at the surface of neutron star.

Conclusion:

Hence, neutrons in the neutron star are in overlapping state.

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Chapter 21 Solutions

Universe

Ch. 21 - Prob. 11CCCh. 21 - Prob. 12CCCh. 21 - Prob. 13CCCh. 21 - Prob. 14CCCh. 21 - Prob. 15CCCh. 21 - Prob. 16CCCh. 21 - Prob. 17CCCh. 21 - Prob. 18CCCh. 21 - Prob. 19CCCh. 21 - Prob. 20CCCh. 21 - Prob. 21CCCh. 21 - Prob. 1QCh. 21 - Prob. 2QCh. 21 - Prob. 3QCh. 21 - Prob. 4QCh. 21 - Prob. 5QCh. 21 - Prob. 6QCh. 21 - Prob. 7QCh. 21 - Prob. 8QCh. 21 - Prob. 9QCh. 21 - Prob. 10QCh. 21 - Prob. 11QCh. 21 - Prob. 12QCh. 21 - Prob. 13QCh. 21 - Prob. 14QCh. 21 - Prob. 15QCh. 21 - Prob. 16QCh. 21 - Prob. 17QCh. 21 - Prob. 18QCh. 21 - Prob. 19QCh. 21 - Prob. 20QCh. 21 - Prob. 21QCh. 21 - Prob. 22QCh. 21 - Prob. 23QCh. 21 - Prob. 24QCh. 21 - Prob. 25QCh. 21 - Prob. 26QCh. 21 - Prob. 27QCh. 21 - Prob. 28QCh. 21 - Prob. 29QCh. 21 - Prob. 30QCh. 21 - Prob. 31QCh. 21 - Prob. 32QCh. 21 - Prob. 33QCh. 21 - Prob. 34QCh. 21 - Prob. 35QCh. 21 - Prob. 36QCh. 21 - Prob. 37QCh. 21 - Prob. 38QCh. 21 - Prob. 39QCh. 21 - Prob. 40QCh. 21 - Prob. 41QCh. 21 - Prob. 42QCh. 21 - Prob. 43QCh. 21 - Prob. 44QCh. 21 - Prob. 45QCh. 21 - Prob. 46QCh. 21 - Prob. 47QCh. 21 - Prob. 48QCh. 21 - Prob. 49QCh. 21 - Prob. 50QCh. 21 - Prob. 51QCh. 21 - Prob. 52QCh. 21 - Prob. 53QCh. 21 - Prob. 54QCh. 21 - Prob. 55QCh. 21 - Prob. 56QCh. 21 - Prob. 57QCh. 21 - Prob. 58QCh. 21 - Prob. 59QCh. 21 - Prob. 60QCh. 21 - Prob. 61QCh. 21 - Prob. 62QCh. 21 - Prob. 63QCh. 21 - Prob. 64QCh. 21 - Prob. 65QCh. 21 - Prob. 66QCh. 21 - Prob. 67QCh. 21 - Prob. 68QCh. 21 - Prob. 69QCh. 21 - Prob. 70QCh. 21 - Prob. 71QCh. 21 - Prob. 72QCh. 21 - Prob. 73QCh. 21 - Prob. 74QCh. 21 - Prob. 75QCh. 21 - Prob. 85QCh. 21 - Prob. 86Q
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