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Physics Lesson 20.1.9 - Average Density of "Nuclear Material"

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Welcome to our Physics lesson on Average Density of "Nuclear Material", this is the ninth lesson of our suite of physics lessons covering the topic of Atomic Nucleus and Its Structural Properties, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Average Density of "Nuclear Material"

Despite the volume of atomic nucleus is much smaller compared to the volume of the atom itself, the mass of atom is almost entirely concentrated in the nucleus (only electrons that are much lighter than protons and neutrons are outside the nucleus). Therefore, the density of atomic nuclei is much greater than the density of the corresponding atoms. Let's clarify this fact through an example.

Example 3

Calculate the average density of nuclear material in a nucleus of atomic mass A.

Solution 3

Assuming the shape of atomic nuclei as spheres, we have for the volume of nuclei in terms of atomic mass A:

V = 4/3 π ∙ r3
= 4/3 π ∙ (r0 ∙ A1/3 )3
= 4/3 π ∙ (1.2 × 10-15 ∙ A1/3 )3
= 7.235 × 10-45 ∙ A [m3]

The density of nuclear material expressed in nucleons per cubic metre is

ρ = A/V
= A/7.235 × 10-45 ∙ A
= 1/7.235 × 10-45 m3
= 1.38 × 1044 nucleons/m3

Since the mass of a nucleon (1 amu therefore) is about 1.6605 × 10-27 kg, we obtain for the density of atomic nuclei in kg/m3:

ρ = 1.38 × 1044 nucleons/m3 × 1.6605 × 10-27 kg/nucleon
= 2.29 × 1017 kg/m3

This value is very large; it is about 2.29 × 1014 times the density of water (103 kg/m3). Another thing to point out here is that we have not specified the type of nuclei in this example. This means that nuclear density is more or less the same for all types of materials. Such high densities are found only in "packed" nuclei that exist only in in heavy stars. In these stars, atoms have lost their electrons due to high temperatures and as a result, the nuclei are much closer to each other than in normal atoms. The average density of such stars ranges from 107 kg/m3 to 1010 kg/m3.

You have reached the end of Physics lesson 20.1.9 Average Density of "Nuclear Material". There are 9 lessons in this physics tutorial covering Atomic Nucleus and Its Structural Properties, you can access all the lessons from this tutorial below.

More Atomic Nucleus and Its Structural Properties Lessons and Learning Resources

Nuclear Physics Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
20.1Atomic Nucleus and Its Structural Properties
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
20.1.1The Atom
20.1.2Thompson's Atomic Model (in 1898)
20.1.3Experiment of Rutherford
20.1.4Bohr's Atomic Model
20.1.5Atomic Nucleus
20.1.6Isotopes and Isobars
20.1.7Atomic Mass (Weight) Number
20.1.8Dimensions of Atomic Nucleus
20.1.9Average Density of "Nuclear Material"

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