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21.1 Nuclear Structure and Stability
The basic idea of nuclear structure was introduced in the chapter on atoms, molecule, and ion.
The number of protons in the nucleus is called the atomic number, and the mass number is called the mass number.
There are different mass numbers for the same element.
A nuclide is referred to by the name of the element followed by a hyphen and a mass number.
The nucleus is small compared to the entire atom, which is 10 to 10 meters.
Nuclei are denser than bulk matter, with an average density of 1.8 x 1014 grams.
Water has a density of 1 gram per cm3 and iridium has a density of 22.6 g/ cm3.
If the average nuclear density was equal to the earth's, the earth's radius would be about 200 meters.
When the core of a very massive star collapses, the star's outer layers explode in a supernova.
They are the densest known stars in the universe, with densities comparable to the average density of an atomic nucleus.
A star with a mass equal to the solar mass of the sun has a diameter of 26 km.
The U-235 nucleus can be treated as a sphere.
The values are similar but the nucleus is more dense than the star.
Find the density of a neutron star with a mass of 1.97 solar mass and a diameter of 13 km and compare it to the density of a hydrogen nucleus, which has a diameter of 1.75 fm.
The star has a density of 3.4 x 1018 kg/m3.
6.0 x 1017 is the density of a hydrogen nucleus.
The hydrogen nucleus is less dense than the neutron star.
Strong attractive forces are needed to hold positively charged protons together in a small nucleus.
There is a force between protons and neutrons.
The attraction between opposite charges is different from the electrostatic force that holds negatively charged electrons around a positively charged nucleus.
The strong nuclear force is much stronger than the electrostatic repulsions between protons, and it is notexistent over larger distances and outside the nucleus.
There are four fundamental forces.
The energy associated with the strong nuclear force can be seen in the helium atom, composed of two protons, two neutrons, and two electrons.
The mass of an 42He atom is less than the combined mass of its six particles.
In the case of helium, the mass defect indicates a loss in mass.
The conversion of mass into energy that is evolved as the atom forms is what leads to the loss in mass.
Nuclear reactions have greater energy changes than chemical reactions.
When matter is converted into energy, this equation can be used.
The 42He nucleus has a mass defect of 0.0305 amu.
The mass-energy equivalence equation can be used to determine the binding energy.
To accommodate the requested energy units, the mass defect must be expressed in kilograms.
The mass defect is 0.0305 g/mol.
To accommodate the units of the other terms in the mass-energy equation, the mass must be expressed in kilograms.
The mass defect is 3.05 x 10-5 kg/mol.
This tremendous amount of energy is associated with the conversion of a very small amount of matter.
Remember that 1 eV is 1.602 x 10-19 J.
The energy changes for breaking and forming bonds are small compared to the energy changes for breaking or forming nuclei, so the mass changes during chemical reactions are not visible.
If a nucleus can't be transformed into another configuration without adding energy from the outside, it's stable.
About 250 nuclides are stable.
The stable isotopes fall into a narrow band according to the plot of the number of neutrons versus the number of protons.
The lighter stable nuclei have the same number of protons and neutrons.
Nitrogen 14 has seven protons and seven neutrons.
The heavier the nucleus, the more neutrons it has.
The stable nuclide lead- 207 has 125 neutrons and 82 protons, an n:p ratio of 1.52, while iron 56 has 30 neutrons and 26 protons, an n:p ratio of 1.15.
Larger nuclei have more repulsions of protons and need larger numbers of neutrons to hold the nucleus together.
The plot shows the nuclides that are stable.
The stable nuclides are shown in blue and the unstable nuclides are shown in green.
All elements with atomic numbers greater than 83 are unstable.
The line is solid
They change spontaneously into other nuclei that are close to the band of stability.
The nature and products of this radioactive decay will be discussed in subsequent sections of this chapter.
There is a relationship between the stability of a nucleus and its structure.
It is more likely that the nucleus is stable if it has even numbers of protons, neutrons, or both.
The complete shells of the nucleus are made by the numbers of protons or neutrons.
The stable electron shells observed for noble gases are similar to these.
Double magic is when he, 8 O, 20 Ca, and 82 Pb are all stable.
The quantum mechanical model of nuclear energy states may be used to rationalize the trends in nuclear stability.
The model is beyond the scope of this chapter.
The nucleus is 28.4 MeV.
The binding energy per nucleon is the largest for nuclides.
The binding energy curve shows that the iron nuclide 56 26 Fe is one of the most stable nuclide.
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