Today, we know that Dalton’s descriptions of atoms were not entirely correct: In Section 2.3 we will see that all atoms of an element are not quite identical, and in Section 2.9 we will see that atoms can change in nuclear reactions. But Dalton’s atomic theory was revolutionary for its time, and it set the theoretical founda- tions for the chemistry that followed, including the experiments of Thomson, Millikan, Rutherford, and many others.
2.3 Isotopes
While Thomson investigated the properties of cathode rays in 1897, other scien- tists designed and built devices to produce beams of positively charged particles.
One of Thomson’s former students, Francis W. Aston (1877–1945), built modified cathode-ray tubes that were evacuated except for small quantities of fill gases such as neon. With these tubes he detected conventional beams of cathode rays, but he also detected secondary beams of positively charged particles. Charge was not the only thing different about the particles in these secondary beams. Whereas cath- ode rays are streams of electrons that all have the same mass and charge regardless of the cathode material or fill gas, the masses of the particles composing Aston’s positive rays did depend on the identity of the fill gas. Aston’s positively charged particles were not individual protons, but rather atoms of the fill gas that had lost electrons to form positively charged ions.
Aston used his positive-ray analyzer (Figure 2.10) to pass positively charged beams of particles through a magnetic field. Each particle in the beam was deflected along a path determined by the particle’s mass: the greater the mass, the smaller the deflection. Using the purest sample of neon gas available, Aston determined that most of the particles had a mass of 20 amu, but about 1 in 10 had a mass of 22 amu.
Since the time of John Dalton, scientists had believed that each element was composed of identical atoms, each having the same mass. Aston’s research con- tradicted this long-held idea. To explain his data, Aston proposed that neon consists of two kinds of atoms, or isotopes. Both isotopes of neon had the same number of protons (10) in the nucleus, but one isotope had 10 neutrons in its nucleus, giving it a mass of 20 amu, whereas the other isotope had 12 neutrons in its nucleus, giving it a mass of 22 amu.
Aston’s work showed that each element is in fact composed of atoms each having the same number of protons in its nucleus, but not necessarily the same number of neutrons, and therefore not the same mass. The number of protons is called the atomic number (Z) of the element. The total number of nucleons (neutrons and protons) in the nucleus of an atom defines its mass number (A). Isotopes of a given element thus all have the same atomic number, Z, but different mass numbers, A. A neu- tral atom has the same number of electrons as protons in its nucleus. The modern periodic table of the elements (inside the front cover of this book) displays the elements in order of atomic number.
isotopes atoms of an element containing different numbers of neutrons.
atomic number (Z) the number of protons in the nucleus of an atom.
nucleon either a proton or a neutron in a nucleus.
mass number (A) the number of nucleons in an atom.
periodic table of the elements a chart of the elements arranged in order of their atomic numbers and in a pattern based on their physical and chemical properties.
Beam of Ne+ ions
20 amu 22 amu Photographic plate Region of electric
and magnetic fields
FIGURE 2.10 Aston’s positive-ray analyzer.
A beam of positively charged ions of neon gas is passed through a focusing slit into a region of electric and magnetic fields.
The ions are separated according to mass:
those with a mass of 20 amu—90% of the sample—hit the detector at one spot, and those with a mass of 22 amu— the remaining 10%—hit the detector at a different spot. Aston’s positive-ray analyzer was the forerunner of the modern mass spectrometer.
2 . 3 Isotopes 53 An atom with a specific combination of neutrons and protons is called a
nuclide. The general symbol for identifying a particular nuclide is
AZX
where X represents the one- or two-letter symbol for the element. For example, the two isotopes of neon identified by Aston have the symbols:
2010Ne 2210Ne
Because Z and X provide the same information— each by itself identifies the element— the subscript Z is frequently omitted: often the isotope symbol is simply written as AX (for example, 20Ne and 22Ne for Aston’s isotopes). This same information— mass number and element name— may also be spelled out. For example, the names of the two isotopes of neon that Aston discovered may be written neon-20 and neon-22.
concePt test
The radioactive atoms measured in the Baby Tooth Survey were strontium-90. Only one of the nuclides below is an isotope of strontium. Which one is it and why?
8738Q 9040X 23490Z
(Answers to Concept Tests are in the back of the book.)
nuclide an atom with particular numbers of neutrons and protons in its nucleus.
SAmpLe eXerCiSe 2.1 Writing nuclide Symbols Lo2 Write symbols in the form AZX for the nuclides that have (a) 6 protons and 6 neutrons, (b) 11 protons and 12 neutrons, and (c) 92 protons and 143 neutrons.
Collect, Organize, and analyze We know the number of protons and neutrons in the nucleus of each nuclide. We need to write symbols in the AZX form, where Z is the atomic number, A is the mass number, and X is the symbol of the element. The number of protons in the nucleus of an atom defines its atomic number (Z) and defines which element it is (X). The sum of the nucleons (protons plus neutrons) is the mass number (A).
Solve
a. This nuclide has six protons, so Z 5 6. It must be an isotope of carbon. Six protons plus six neutrons give the isotope a mass number of 12, which makes it carbon-12,
126C.
b. This nuclide has 11 protons, which means Z 5 11, so it must be an isotope of sodium. Eleven protons and 12 neutrons give the isotope a mass number of 23, so the isotope is sodium-23, 2311Na.
c. This nuclide has 92 protons, so Z 5 92, which makes it an isotope of uranium. The mass number is 92 1 143 5 235. This isotope is uranium-235, 23592U.
Think about It In working through this exercise, did you use the periodic table of the elements? Once you identify the number of protons in a nucleus (its atomic number), finding a symbol and identifying the element it represents is easy because the elements in the periodic table are arranged in order of increasing atomic number.
d Practice Exercise Use the format AX to write the symbols of the nuclides having (a) 26 protons and 30 neutrons, (b) 7 protons and 8 neutrons, (c) 17 protons and 20 neutrons, and (d) 19 protons and 20 neutrons.
(Answers to Practice Exercises are in the back of the book.)
2.4 Average Atomic Mass
Each element in the periodic table is represented by its symbol. The number above the symbol is the element’s atomic number (Z), and the number below the symbol is the element’s average atomic mass. More precisely, the number below the sym- bol is the weighted average of the masses of all the isotopes of the element.
To understand the meaning of a weighted average, consider the masses and natural abundances of the three isotopes of neon in the table shown here. Nat- ural abundances are usually expressed in percentages. Thus, 90.4838% of all neon atoms are neon-20, 9.2465% are neon-22, and only 0.2696% are neon-21.
The abundance of neon-21 is so small that Aston could not detect it with his positive-ray analyzer. Modern mass spectrometers, which are the source of nat- ural abundance data such as these, are vastly more sensitive and more precise than Aston’s prototype.
To determine the average atomic mass of any element, we multiply the mass of each isotope by its natural abundance (in the language of mathematics, we weight the isotope’s mass by using natural abundance as the weighting factor) and then sum the three weighted masses. To simplify the calculation for neon, we convert the percent abundance values into their decimal equivalents:
Average atomic mass of neon 5 (19.9924 amu 3 0.904838) 5 18.08988
1 (20.9940 amu 3 0.002696) 5 0.05660
1 (21.9914 amu 3 0.092465) 5 2.03344
20.17996 amu
or, accounting for significant figures, 20.1800 amu. No atom of neon has the average atomic mass; every atom of neon in the universe must have a mass equal to that of one of the three neon isotopes. The value we have calculated is simply the weighted average of these three isotopic masses.
Isotope
Mass (amu)
Natural abundance
(%) Neon-20 19.9924 90.4838
Neon-21 20.9940 0.2696
Neon-22 21.9914 9.2465
SAmpLe eXerCiSe 2.2 Determining the number of neutrons in a nuclide
Lo2
How many neutrons are in each of the following nuclides: (a) 14N; (b) 32P; (c) 157Gd?
Collect, Organize, and analyze We are given the symbols of three nuclides and asked to determine the number of neutrons in each of their nuclei. We know the value of Z from the element’s symbol. Subtracting Z from A gives us the number of neutrons.
Solve
a. 14N is a nuclide of nitrogen, whose atoms each have seven protons. The number of neutrons is A 2 Z 5 14 2 7 5 7.
b. 32P is a nuclide of phosphorus (Z 5 15) with 32 nucleons per nucleus. The number of neutrons is 32 2 15 5 17.
c. 157Gd is a nuclide of gadolinium (Z 5 64). The number of neutrons is 157 2 64 5 93.
Think about It These three nuclides illustrate a trend among stable nuclei: the ratios of neutrons to protons in stable nuclei increase as atomic number increases.
d Practice Exercise Determine the number of protons and neutrons in each of these radioactive nuclides: (a) 60Co, used in cancer therapy; (b) 131I, used in thyroid therapy; (c) 192Ir, used to treat coronary disease.
(Answers to Practice Exercises are in the back of the book.) average atomic mass a weighted
average of the masses of all the isotopes of an element, calculated by multiplying the natural abundance of each isotope by its mass in atomic mass units and then summing these products.
natural abundance the proportion of a particular isotope, usually expressed as a percentage, relative to all the isotopes of that element in a natural sample.
2 .5 The Periodic Table of the Elements 55 This method of calculating average atomic mass works for every element. The
general formula for these calculations is
mX5a1m11a2m21a3m31. . . (2.1) where mX is the average atomic mass of element X, which has isotopes with masses m1, m2, m3, . . . , the natural abundances of which, expressed in decimal form, are a1, a2, a3, . . . .
2.5 The Periodic Table of the Elements
Long before chemists knew about electrons, protons, and neutrons, they knew that groups of elements, such as Li, Na, and K, or F, Cl, and Br, had similar chemical (and sometimes physical) properties. When the elements were arranged
SAmpLe eXerCiSe 2.3 calculating an average atomic Mass Lo3 Although strontium-90 does not occur in nature, there are four naturally occurring isotopes of strontium: 84Sr, 86Sr, 87Sr, and 88Sr. Calculate the average atomic mass of strontium (Z 5 38), given that its stable isotopes have these natural abundances:
Symbol Mass (amu) Natural abundance (%)
84Sr 83.9134 0.56
86Sr 85.9094 9.86
87Sr 86.9089 7.00
88Sr 87.9056 82.58
Collect, Organize, and analyze We know the masses and natural abundances of each of the four isotopes of strontium, and we can combine these data by using Equation 2.1 to calculate average atomic mass.
Solve
Average atomic mass 5 (83.9134 amu 3 0.0056) 5 0.470 amu 1 (85.9094 amu 3 0.0986) 5 8.471 amu 1 (86.9089 amu 3 0.0700) 5 6.083 amu 1 (87.9056 amu 3 0.8258) 5 72.592 amu
87.616 amu
We have retained one more digit than is significant to avoid rounding errors in the calculation, so adjusting for the correct number of significant figures, we report the answer as 87.62 amu.
Think about It Note that the four values of natural abundances expressed as decimals should add up to 1.0000, and they do. Sometimes this is not the case (check the neon abundances earlier). Uncertainties in the last decimal place may be due to uncertainties in measured or calculated values or in rounding them off. The calculated average atomic mass of strontium is consistent with the value given inside the front cover.
d Practice Exercise Silver (Ag) has two stable isotopes: silver-107 (106.905 amu) and silver-109 (108.905 amu). If the average atomic mass of silver is 107.868 amu, what is the natural abundance of each isotope? Hint: Let x be the natural abundance of one of the isotopes. Then 1 2 x is the natural abundance of the other.
(Answers to Practice Exercises are in the back of the book.)
by increasing atomic mass, repeating patterns of similar properties appeared among the elements. This periodicity in the chemical properties of the elements inspired several 19th-century scientists to create tables of the elements in which the elements were arranged in patterns based on similarities in their chemical properties.
The most successful of these scientists was the Russian chemist Dmitri Mendeleev (1834–1907). In 1872 he published a table (Figure 2.11) that was the forerunner of the modern periodic table (Figure 2.12). In addition to organizing all the elements that were known at the time, Mendeleev realized that there might be elements in nature that were yet to be discovered, so he left empty cells in his table for those unknown elements. Doing so allowed him to align the known elements so that those in each column had similar chemical properties. On the basis of the locations of the empty cells, Mendeleev predicted the chemical properties of the missing elements that ultimately were discovered. Note that Mendeleev arranged the elements in his periodic table in order of increasing atomic mass. In modern periodic tables the elements appear in order of increasing atomic number.
concePt test
Why did Mendeleev skip cells in his periodic table?
(Answers to Concept Tests are in the back of the book.)
Navigating the Modern Periodic Table
The modern periodic table (Figure 2.12) contains seven horizontal rows (also called periods) and 18 columns (known as groups or families) of elements. The periods are numbered at the far left of each row, and the group numbers appear at the top of each column. The periodic table inside the front cover shows a second set of column headings containing numbers followed by the letter A or B. These secondary headings were widely used in earlier versions of the table, and many scientists (and students) still find them useful.
The elements in the periodic table are also divided into three broad catego- ries highlighted by the three colors in Figure 2.12. Elements highlighted in tan
are metals. They tend to conduct heat and electricity well; they tend to be malleable (capable of being shaped by hammering) or ductile (capable of being drawn out in a wire), and they are shiny solids at room temperature, except for mercury (Hg), which is a liquid at room temperature (Figure 2.13a). Elements highlighted in blue are nonmetals. They are poor conductors of heat and elec- tricity; the solids among them tend to be brittle, and most are gases at room temperature, except for bromine, which is a liquid with a low boiling point (Figure 2.13b). Lastly, the elements highlighted in green are called metalloids or semimetals, so named because they tend to have the physical properties of metals but the chemical properties of nonmetals (Figure 2.13c).
period a horizontal row in the periodic table.
group all the elements in the same column of the periodic table; also called family.
metals the elements on the left side of the periodic table that are typically shiny solids that conduct heat and electricity well and are malleable and ductile.
nonmetals elements with properties opposite those of metals, including poor conductivity of heat and electricity.
metalloids (also called semimetals) elements along the border between metals and nonmetals in the periodic table; they have some metallic and some nonmetallic properties.
main group elements (also called representative elements) the elements in groups 1, 2, and 13 through 18 of the periodic table.
transition metals the elements in groups 3 through 12 of the periodic table.
3 2 1
4 5 6 7 8 9 10 11 12
H1 Li7
Be9.4 11B
12C 14N
16O 19F Na23
Mg24 27.3Al
Si28 31P
32S 35.5Cl 39K
Ca40 44? Ti48
51V Cr52
Mn55 Cu63
Zn65 68?
72? As75
Se78 Br80 Rb85
Sr ?Yt 87 88
Zr90 Nb94
Mo96 100 ? 108Ag
112Cd 113In
118Sn 122Sb
125Te 127J 133Cs
137Ba
?Di138
?Ce140
178 ?Er 180?La
182Ta 184W 199Au
200Hg 204Tl
207Pb 208Bi 231Th
240U I
Group Number