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# Isotopes and Nuclear Stability

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The nuclei of atoms contain protons and neutrons while electron clouds surrounding the nuclei contain  the electrons . The positively charged protons are very close together in an atomic nucleus and the repulsive force of the like charges is tremendous. The strong force is a type of interaction that binds together protons and neutrons. Without the strong force, the positively charged protons would blow the nucleus apart.

### Isotopes

Until 1932, the positively charged nucleus  of an atom was known to exist, but it was believed to contain only protons. The nucleus was known to be surrounded by enough negatively charged electrons to make the atom electrically neutral. Most of the atom was empty space, with its mass concentrated in the tiny nucleus.

Twelve years earlier, Lord Ernest Rutherford, a pioneer in atomic structure, had postulated the existence of a third, neutral, sub-atomic particle, with the approximate mass of a proton, that could result from the capture of an electron by a proton. This postulation stimulated a search for the particle. However, its electrical neutrality complicated the search because almost all experimental techniques of this period measured charged particles.

James Chadwick bombarded hydrogen atoms in paraffin with beryllium emissions. By comparing the energies of recoiling charged particles from different targets, he proved that the beryllium emissions contained a neutral component with a mass approximately equal to that of the proton. He called it the neutron in a paper published in 1932.

Since the identification of the neutron, the model of the atomic nucleus has changed very little. According to this model, a nucleus is considered to be an aggregate of protons and neutrons. A proton has a positive charge of  $1.6 \times 10^{-19} \ C$ and a mass of $1.673 \times 10^{-27} \ kg$ . The neutron is electrically neutral and has a mass of $1.675 \times 10^{-27} \ kg$ . These two constituents of a nucleus are referred to collectively as nucleons.

Although the hydrogen nucleus consists of a single proton, the nuclei of all other elements contain both neutrons and protons. The different types of nuclei are referred to as nuclides . The number of protons in a nucleus is called the atomic number and is designated by the symbol $Z$ . The total number of nucleons, neutrons and protons, is designated by the symbol  $A$ and is called the mass number . A nuclide with 7 protons and 8 neutrons thus has  $Z = 7$ and $A = 15$ . The number of neutrons, $N$ , is $N = A- Z$ . To specify a given nuclide, we need give only  $A$ and $Z$ . These can be shown in a complete nuclear symbol which takes the form

$^A_Z X$

where  $X$ is the chemical symbol for the element,  $A$ is the mass number, and  $Z$ is the atomic number. For example, a nitrogen nucleus containing 7 protons and 8 neutrons would be $^{15}_7 N$ . Since all nitrogen atoms have 7 protons in their nucleus, sometimes the 7 is omitted and the symbol is written simply as $^{15} N$ . This same nuclide is also sometimes written as nitrogen-15.

The identity of an atom is determined by the number of protons in the nucleus. All hydrogen atoms must have exactly 1 proton in the nucleus. The number of neutrons in the nuclei of atoms of a particular element, however, may vary. For example, a hydrogen atom will always have 1 proton, but may have zero, one, or two neutrons in the nucleus - as long as it has 1 proton, it is a hydrogen atom.

Nuclei that have the same number of protons in the nucleus but a different number of neutrons are called isotopes . Hydrogen has three isotopes.

$& ^1_1 H \qquad ^2_1 H \qquad ^3_1 H$

One isotope of hydrogen has 1 proton and 0 neutrons in the nucleus so it has a mass number of 1. Another isotope of hydrogen has 1 proton and 1 neutron in the nucleus so it has a mass number of 2. The third isotope of hydrogen has 1 proton and 2 neutrons in the nucleus so it has a mass number of 3. (The isotope of hydrogen with a mass number of 2 is sometimes called deuterium and the isotope of hydrogen with a mass number of 3 is sometimes called tritium, but they are all hydrogen.) Carbon has six isotopes; carbon-11, carbon-12, carbon-13, carbon-14, carbon-15, and carbon-16. The isotopes of a given element are not all equally abundant. For example, 98.9% of all naturally occurring carbon is carbon-12 and about 1.1% is carbon-13. The other isotopes of carbon are even less abundant.

The periodic table is a complete listing of all the known elements.

Each element has its own square in the periodic table. The square contains the chemical symbol for the element, the atomic number, and the atomic weight . The atomic weight of an element is a weighted average of its isotopes.

Example Problem:

The element boron consists of two isotopes, boron-10 and boron-11. The abundance of boron-10 is 20.0% and the abundance of boron-11 is 80.0%. What is the atomic weight of boron?

Solution:

$\text{Atomic weight} = (0.20)(10.0 \text{ amu}) + (0.80)(11.0 \text{ amu}) = 2.0 + 8.8 = 10.8 \text{ amu}$

#### Summary

• Since the identification of the neutron, the model of the atomic nucleus has changed very little. According to this model, a nucleus is considered to be an aggregate of protons and neutrons.
• The number of protons in a nucleus is called the atomic number and is designated by the symbol $Z$ .
• The total number of nucleons, neutrons and protons, is designated by the symbol  $A$ and is called the mass number.
• The number of neutrons, $N$ , is $N = A - Z$ .
• Nuclei that have the same number of protons in the nucleus but a different number of neutrons are called isotopes.
• Each element has its own square in the periodic table.
• Each elemental square on the periodic table contains the chemical symbol for the element, the atomic number, and the atomic weight.
• The atomic weight of an element is a weighted average of its isotopes.

#### Practice

1. Nucleus #1 has 6 protons and a mass number of 14 while nucleus #2 has 7 protons and a mass number of 14.  Are these isotopes or are they nuclei of different elements?
2. Nucleus #1 has 5 protons and a mass number of 12 while nucleus #2 has 5 protons and a mass number of 13.  Are these isotopes or are they nuclei of different elements?

#### Review

1. What do different isotopes of a given element have in common? How are they different?
2. What is the element name of the atom represented by $^{232}_{92} X$ ?
3. How many protons and how many neutrons does the nucleus in problem #2 have?
4. Using the following data, calculate the atomic weight of magnesium.

Magnesium-24 = 78.70%

Magnesium-25 = 10.13%

Magnesium-26 = 11.17%