14.2: The Atomic Nucleus
- Page ID
- 478406
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Explain the atomic number, mass number, and isotopes as it relates to the particles within the nucleus of an atom.
- Calculate the average atomic mass.
We introduced the idea of an atomic nucleus in a previous chapter. Now we will discuss this part of the atom in more detail. Although the electrons are responsible for the chemical reactions of elements. The particles inside the nucleus are important to understand for other changes, such as nuclear radiation. These particles are collectively called nucleons, and consist of protons and neutrons. In this section we will discuss a few ways we keep track of and discuss the particles within the nucleus.
Atomic Number
The atomic number (Z) of an element is the number of protons in the nucleus of each atom of that element. This means that the number of protons is the characteristic which makes each element unique compared to all other elements. Elements are different because of their atomic number. The periodic table displays all of the known elements and is arranged in order of increasing atomic number. In this table, an element's atomic number is indicated above the elemental symbol. Hydrogen, at the upper left of the table, has an atomic number of 1. Every hydrogen atom has one proton in its nucleus. Following on the table is helium, whose atoms have two protons in the nucleus. Lithium atoms have three protons, and so forth.
Mass Number
Rutherford showed that the vast majority of the mass of an atom is concentrated in its nucleus, which is composed of protons and neutrons. The mass number (A) is defined as the total number of protons and neutrons in an atom. It can be calculated by adding the number of neutrons and the number of protons (atomic number) together.
Mass number = atomic number + number of neutrons
Consider Table \(\PageIndex{1}\) below that shows data from the first six elements of the periodic table.
| Name | Symbol | Protons | Neutrons | Electrons | Atomic Number | Mass Number |
|---|---|---|---|---|---|---|
| Hydrogen | \(\ce{H}\) | 1 | 0 | 1 | 1 | 1 |
| Helium | \(\ce{He}\) | 2 | 2 | 2 | 2 | 4 |
| Lithium | \(\ce{Li}\) | 3 | 4 | 3 | 3 | 7 |
| Beryllium | \(\ce{Be}\) | 4 | 5 | 4 | 4 | 9 |
| Boron | \(\ce{B}\) | 5 | 6 | 5 | 5 | 11 |
| Carbon | \(\ce{C}\) | 6 | 6 | 6 | 6 | 12 |
Consider the element helium. Its atomic number is 2, so it has two protons in its nucleus. Its nucleus also contains two neutrons. Since \(2 + 2 = 4\), we know that the mass number of the helium atom is 4. Finally, the helium atom also contains two electrons since the number of electrons must equal the number of protons. This example may lead you to believe that atoms have the same number of protons and neutrons, but further examination of the table above will show that this is not the case. Lithium, for example, has three protons and four neutrons, leaving it with a mass number of 7.
Knowing the mass number and the atomic number of an atom allows you to determine the number of neutrons present in that atom by subtraction.
\[\text{Number of neutrons} = \text{mass number} - \text{atomic number}\nonumber \]
Example \(\PageIndex{1}\)
Atoms of the element chromium \(\left( \ce{Cr} \right)\) have an atomic number of 24 and a mass number of 52. How many neutrons are in the nucleus of a chromium atom?
Solution
To determine this, you subtract the atomic number from the mass number, as shown above:
\[52 - 24 = 28 \: \text{neutrons in a chromium atom}\nonumber \]
The composition of any atom can be illustrated with a shorthand notation using the atomic number and the mass number. Both are written before the chemical symbol, with the mass number written as a superscript and the atomic number written as a subscript. The chromium atom discussed above would be written as:
\[\ce{^{52}_{24}Cr}\nonumber \]
Another way to refer to a specific atom is to write the mass number of the atom after the name, separated by a hyphen. The above atom would be written as chromium-52.
Isotopes
Although John Dalton stated in his atomic theory of 1804 that all atoms of an element are identical, the discovery of the neutron began to show that this assumption was not correct. The study of radioactive materials (elements that spontaneously give off particles to form new elements) by Frederick Soddy (1877-1956) gave important clues about the internal structure of atoms. His work showed that some substances with different radioactive properties and different atomic masses were in fact the same element. He coined the term isotope from the Greek roots isos (íσος “equal”) and topos (τóπος “place”). He described isotopes as, “Put colloquially, their atoms have identical outsides but different insides.” Soddy won the Nobel Prize in Chemistry in 1921 for his work.
As stated earlier, not all atoms of a given element are identical. Specifically, the number of neutrons can be variable for many elements. As an example, naturally occurring carbon exists in three forms. Each carbon atom has the same number of protons (6), which is its atomic number. Each carbon atom also contains six electrons in order to maintain electrical neutrality. However the number of neutrons varies as six, seven, or eight. Isotopes are atoms that have the same number atomic number, but different mass numbers due to a change in the number of neutrons.
When referring to a single type of nucleus, we often use the term nuclide and identify it by the notation \(\ce{_{A}^{Z}X}\), where \(X\) is the symbol for the element, \(A\) is the mass number, and \(Z\) is the atomic number (for example, \(\ce{^{14}_6C}\)). Often a nuclide is referenced by the name of the element followed by a hyphen and the mass number. For example, \(\ce{^{14}_6C}\) is called “carbon-14.”
The other two isotopes of carbon can be referred to as carbon-12 (\(^{12} _6C\)), and carbon-13 (\(^{13} _6C\)). A carbon atom is one of these three different nuclides. Most elements naturally consist of combinations of isotopes. Carbon has three natural isotopes, while some heavier elements can have many more. Tin has ten stable isotopes, the most of any element.
While the presence of isotopes affects the mass of an atom, it does not affect its chemical reactivity. Chemical behavior is governed by the number of electrons and the number of protons. Carbon-13 behaves chemically in exactly the same way as the more plentiful carbon-12.
)
Mass Number
Average Atomic Mass
Most elements occur naturally as a mixture of two or more isotopes. The table below shows the natural isotopes of several elements, along with the percent natural abundance of each.
| Element | Isotope (Symbol) | Percent Natural Abundance | Atomic Mass \(\left( \text{amu} \right)\) | Average Atomic Mass \(\left( \text{amu} \right)\) |
|---|---|---|---|---|
| Hydrogen | \(\ce{_1^1H}\) | 99.985 | 1.0078 | 1.0080 |
| \(\ce{_1^2H}\) | 0.015 | 2.0141 | ||
| \(\ce{_1^3H}\) | negligible | 3.0160 | ||
| Carbon | \(\ce{_6^{12}C}\) | 98.89 | 12.000 | 12.011 |
| \(\ce{_6^{13}C}\) | 1.11 | 13.003 | ||
| \(\ce{_6^{14}C}\) | trace | 14.003 | ||
| Oxygen | \(\ce{_8^{16}O}\) | 99.759 | 15.995 | 15.999 |
| \(\ce{_8^{17}O}\) | 0.037 | 16.995 | ||
| \(\ce{_8^{18}O}\) | 0.204 | 17.999 | ||
| Chlorine | \(\ce{_{17}^{35}Cl}\) | 75.77 | 34.969 | 35.453 |
| \(\ce{_{17}^{37}Cl}\) | 24.23 | 36.966 | ||
| Copper | \(\ce{_{29}^{63}Cu}\) | 69.17 | 62.930 | 63.546 |
| \(\ce{_{29}^{65}Cu}\) | 30.83 | 64.928 |
For some elements, one particular isotope predominates greatly over the other isotopes. Naturally occurring hydrogen is nearly all hydrogen-1 and naturally occurring oxygen is nearly all oxygen-16. For many other elements, however, more than one isotope may exist in more substantial quantities. Chlorine (atomic number 17) is a yellowish-green toxic gas. About three quarters of all chlorine atoms have 18 neutrons, giving those atoms a mass number of 35. About one quarter of all chlorine atoms have 20 neutrons, giving those atoms a mass number of 37. Were you to simply calculate the arithmetic average of the precise atomic masses, you would get 36.
\[\frac{\left( 34.969 + 36.966 \right)}{2} = 35.968 \: \text{amu}\nonumber \]
Clearly the actual average atomic mass from the last column of the table is significantly lower. Why? We need to take into account the percent natural abundance of each isotope, in order to calculate the weighted average. The atomic mass of an element is the weighted average of the atomic masses of the naturally occurring isotopes of that element. The sample problem below demonstrates how to calculate the atomic mass of chlorine.
Example \(\PageIndex{1}\)
Use the atomic masses of each of the two isotopes of chlorine along with their respective percent abundances to calculate the average atomic mass of chlorine.
Solution
Step 1: List the known and unknown quantities and plan the problem.
Known
- Chlorine-35: atomic mass \(= 34.969 \: \text{amu}\) and percent abundance \(= 75.77\%\)
- Chlorine-37: atomic mass \(= 36.966 \: \text{amu}\) and percent abundance \(= 24.23\%\)
Unknown
- Average atomic mass of chlorine
Change each percent abundance into decimal form by dividing by 100. Multiply this value by the atomic mass of that isotope. Add together for each isotope to get the average atomic mass.
Step 2: Calculate.
\[\begin{array}{ll} \text{chlorine-35} & 0.7577 \times 34.969 = 26.50 \: \text{amu} \\ \text{chlorine-37} & 0.2423 \times 36.966 = 8.957 \: \text{amu} \\ \text{average atomic mass} & 26.50 + 8.957 = 35.46 \: \text{amu} \end{array}\nonumber \]
Note: Applying significant figure rules results in the \(35.45 \: \text{amu}\) result without excessive rounding error. In one step:
\[\left( 0.7577 \times 34.969 \right) + \left(0.2423 \times 36.966 \right) = 35.46 \: \text{amu}\nonumber \]
Step 3: Think about your result.
The calculated average atomic mass is closer to 35 than to 37 because a greater percentage of naturally occurring chlorine atoms have the mass number of 35. It agrees with the value from the table above.
Section Summary
- Rutherford proposed a model of the atomic nucleus which had a solid core.
- The atomic number (Z) of an element is the number of protons in the nucleus of each atom of that element.
- The number of electrons is equal to the number of protons in an atom of an element.
- The mass number is defined as the total number of protons and neutrons in an atom.
- The mass number = number of neutrons + atomic number.
- Isotopes are atoms that have the same atomic number, but different mass numbers due to a change in the number of neutrons.
- The term nuclide refers to the nucleus of a given isotope of an element.
- The atomic mass of an atom equals the sum of the protons and the neutrons.
- The atomic mass of an element is the weighted average of the atomic masses of the naturally occurring isotopes of that element.
- Calculations of atomic mass use the percent abundance of each isotope.
Glossary
- nucleons
- The particles inside the nucleus of an atom (protons and neutrons).
- mass number (A)
- The total number of protons and neutrons in an atom.
- atomic number (Z)
- The number of protons in the nucleus of each atom of that element.
- isotopes
- Atoms which have the same number of protons (and hence atomic number), but different number of neutrons (and hence different mass numbers).
- nuclide
- A single type of atomic nucleus.
- atomic mass
- The weighted average of all of the naturally occurring isotopes of a given element.