Conceptual Physics

Step-by-step solution

We begin by converting the mass of the hydrogen nucleus into kilograms, then we calculate the radius of the nucleus. Using the radius, we

calculate the nuclear volume. Finally, we divide the mass by the volume to determine the density.

Now perform the same calculations for aluminum.

The densities are nearly identical. This is further confirmation that nucleons are tightly packed and incompressible.

The nuclear density is far beyond the density of materials in our experience. For example, consider gold, which is 19.3 times denser than water

and almost 1.7 times as dense as lead. A nucleus is 12,000,000,000,000 times denser than gold. (In case you were wondering, no, the zero

key did not get stuck down while we typed that number.) Recall that Rutherford found that the atomic radius was on the order of 10,000 times

the nuclear radius. The volume of a sphere scales as the cube of the radius, so the ratio of atomic to nuclear volume is approximately (10,000)

(^3). Since the mass of an atom mostly resides in the nucleus, and so much of an atom is empty, this explains the incredible density of a nucleus.

Step Reason

1. mH = 1u = 1.66×10í^27 kg hydrogen nuclear mass, definition of u

2. R = (1.2×10í^15 m)A1/3 apply nuclear radius equation

3. calculate volume of hydrogen nucleus

4. definition of density

Step Reason

5. mAl = 27 u = 27(1.66×10í^27 kg) aluminum nuclear mass, definition of u

6. R = (1.2×10í^15 m)A1/3 apply nuclear radius equation

7. calculate volume of aluminum nucleus

8. definition of density

38.8 - Stable nuclei

What are the rules for the number of allowed protons and neutrons in a nucleus? Is any combination of protons and neutrons possible? Could

there be a hydrogen atom whose nucleus has 1 proton and 7 neutrons? What about a silver atom with 47 protons and no neutrons? Could

there be an element with 150 protons and any number of neutrons?

The nuclei described above do not exist. You could not even momentarily create nuclei with such extreme imbalances of protons and neutrons,

or in the last case, a nucleus with so many protons. Only certain combinations of protons and neutrons can form nuclei, and even fewer

combinations can form stable nuclei.

Bystable, we mean elements that will not spontaneously decay. Gold-197 is the only stable isotope of gold, while there are several stable

oxygen isotopes: oxygen-16, oxygen-17 and oxygen-18.

(^704) Copyright 2007 Kinetic Books Co. Chapter 38