Atomic Mass Of First 50 Elements

The atomic mass is useful in chemistry when it is paired with the mole concept: the atomic mass of an element, measured in amu, is the same as the mass in grams of one mole of an element. Thus, since the atomic mass of iron is 55.847 amu, one mole of iron atoms would weigh 55.847 grams. Answered 2 years ago Author has 623 answers and 295.3K answer views The atomic mass of the first 50 elements is 2852. This is 1+4+7+9+11 et alii. Note: the question does not ask for the atomic MASSES of the first 50 elements. Zenith zd309y9 dehumidifier manual. This is a list of chemical elements, sorted by atomic mass (or most stable isotope) and color coded according to type of element.Each element's atomic number, name, element symbol, and group and period numbers on the periodic table are given. The number in parenthesis gives the uncertainty in the 'concise notation' dis given in parenthesis next to the least significant digits to which it.

Elements and Atoms: Chapter 12
Mendeleev's First Periodic Table

Dmitrii Mendeleev (1834-1907; see portrait of Mendeleev in 1878 by Kramskoy) was born in Tobolsk, in Western Siberia. His chief contribution to chemistry was the establishment of the periodic system of elements. Mendeleev was one of a number of independent discoverers of the periodic law in the 1860s--that number ranging from one [Leicester 1948] to six [van Spronsen 1969] depending on the criteria one adopts. Mendeleev's formulation was clearly superior in several respects to the work of contemporary classifiers: it was the clearest, most consistent, and most systematic formulation, and Mendeleev made several testable predictions based on it. It was not, however, free from error. Scientists, even great scientists, trying to see further than others have in the past, do not always see the whole picture clearly. As noted below, Mendeleev himself corrected some of the errors within a few years; others persisted well into the 20^th century.

This table and the accompanying observations were first presented to the Russian Chemical Society in March 1869. (Actually, Mendeleev was ill, and his colleague Nikolai Menshutkin presented his paper [Menschutkin 1934].) The paper was published in the first volume of the new society's journal. That same year, a German abstract of the paper, consisting of the table and eight comments, was published in Zeitschrift für Chemie. The German abstract was the vehicle by which Mendeleev's ideas reached chemists working in Western Europe. An English translation of that German abstract is presented here. View a manuscript draft of the table.

On the Relationship of the Properties of the Elements to their Atomic Weights

D. Mendelejeff, Zeitschrift für Chemie12, 405-406 (1869); translation by Carmen Giunta

By ordering the elements according to increasing atomic weight in vertical rows so that the horizontal rows contain analogous elements,[1] still ordered by increasing atomic weight, one obtains the following arrangement, from which a few general conclusions may be derived.

Ti=50	Zr=90	?[2]=180
V=51	Nb=94	Ta=182
Cr=52	Mo=96	W=186
Mn=55	Rh=104,4[3]	Pt=197,4[4]
Fe=56	Ru=104,4	Ir=198
Ni=Co=59	Pd=106,6	Os=199
H=1[5]	Cu=63,4	Ag=108	Hg=200
Be=9,4	Mg=24	Zn=65,2	Cd=112
B=11	Al=27,4	?[6]=68	Ur=116[7]	Au=197?
C=12	Si=28	?[8]=70	Sn=118
N=14	P=31	As=75	Sb=122	Bi=210?
O=16	S=32	Se=79,4	Te=128?
F=19	Cl=35,5	Br=80	J=127[9]
Li=7	Na=23	K=39	Rb=85,4	Cs=133	Tl=204
Ca=40	Sr=87,6	Ba=137	Pb=207
?[10]=45	Ce=92[11]
?Er=56	La=94
?Yt=60	Di=95
?In=75,6	Th=118?

1. The elements, if arranged according to their atomic weights, exhibit an evident stepwise variation[12] of properties.
2. Chemically analogous elements have either similar atomic weights[13] (Pt, Ir, Os), or weights which increase by equal increments (K, Rb, Cs).[14]
3. The arrangement according to atomic weight corresponds to the valence[15] of the element and to a certain extent the difference in chemical behavior, for example Li, Be, B, C, N, O, F.
4. The elements distributed most widely in nature have small atomic weights[16], and all such elements are marked by the distinctness of their behavior. They are, therefore, the representative elements; and so the lightest element H is rightly chosen as the most representative.
5. The magnitude of the atomic weight determines the properties of the element. Therefore, in the study of compounds, not only the quantities and properties of the elements and their reciprocal behavior is to be taken into consideration, but also the atomic weight of the elements. Thus the compounds of S and Tl [sic--Te was intended], Cl and J, display not only analogies, but also striking differences.[17]
6. One can predict the discovery of many new elements, for example analogues of Si and Al with atomic weights of 65-75.[18]
7. A few atomic weights will probably require correction; for example Te cannot have the atomic weight 128, but rather 123-126.[19]
8. From the above table, some new analogies between elements are revealed. Thus Bo (?) [sic--apparently Ur was intended] appears as an analogue of Bo and Al, as is well known to have been long established experimentally.

(Russian Chemical Society 1, 60)

Notes

[1]The principle of periodicity is apparent in this first sentence: repetition of chemical properties in a series of elements arranged by atomic weight. Note also the cosmetic difference between Mendeleev's layout and that of modern tables, which order the elements in horizontal rows such that families of elements appear in vertical columns. Mendeleev would use the latter sort of layout before long [Mendeleev 1871].

[2]This table contains several implicit predictions of unknown elements. Mendeleev soon retreated from this prediction of a heavier analogue of titanium and zirconium. His later tables [Mendeleev 1871] erroneously placed lanthanum in this spot. This original prediction was actually borne out in 1923 with the discovery of hafnium.

[3]Rhodium (Rh) is misplaced. It belongs between ruthenium (Ru) and palladium (Pd). Technetium (Tc), the element which belongs between ruthenium and molybdenum (Mo) has no stable isotopes and was not synthesized until 1937. Srs iwow 3 3 1 keygen generator.

[4]Most of the elements in this column are slightly out of order. After tungsten (W) should come rhenium (Re), which was not yet discovered, followed by osmium (Os), iridium (Ir), platinum (Pt), gold (Au), mercury (Hg), thallium (Tl), lead (Pb), and bismuth (Bi). Bismuth, however, is placed correctly insofar as it completes the row beginning with nitrogen (N). At this time, lead was frequently miscategorized, placed among elements which form compounds with one atom of oxygen (PbO analogous to CaO, for example); however, lead also forms a compound with two atoms of oxygen (PbO₂ analogous to CO₂) and it belongs in the same group as carbon (C). Similarly, thallium was often placed among elements which form compounds with one atom of chlorine (TlCl analogous to NaCl, for example); however, thallium also forms a compound with three atoms of chlorine (TlCl₃ analogous to BCl₃) and it belongs in the same group as boron (B).

[5]The classification of hydrogen has been an issue throughout the history of periodic systems. Some tables place hydrogen with the alkali metals (lithium, sodium, etc.), some with the halogens (fluorine, chlorine, etc.), some with both, and some in a box of its own detached from the main body of the table. Mendeleev's original table did none of the above, placing it in the same row as copper, silver, and mercury.

[6]The prediction of an unknown analogue of aluminum was borne out by the discovery in 1875 of gallium (atomic weight = 70), the first of Mendeleev's predictions to be so confirmed. [Lecoq de Boisbaudran 1877]

[7]Uranium (standard symbol U) is misplaced. Its atomic weight is actually more than double the value given here. The element which belongs between cadmium (Cd) and tin (Sn) is indium (In), and Mendeleev put indium there in the next version of his table [Mendeleev 1871]. The proper place for uranium, however, would not be found until the 1940s.

[8]The prediction of an unknown analogue of silicon was borne out by the discovery in 1886 of germanium (atomic weight = 73). [Winkler 1886]

[9]In German publications, J is frequently used instead of I as the chemical symbol for iodine (Jod, in German). Iodine is placed correctly after tellurium (i.e., with the halogens) despite having a lower atomic weight than tellurium. See comment 7 after the table.

[10]The prediction of an unknown element following calcium is a weak version of Mendeleev's subsequent prediction of the element we now know as scandium, discovered in 1879 [Nilson 1879]. In Mendeleev's 1871 table [Mendeleev 1871] the missing element is correctly placed between calcium and titanium, and as an analogue of yttrium. That the 1869 prediction is flawed can be seen from the fact that every other entry in the bottom reaches of the table is wrong. (See next note.) Still, the prediction deserves more credit than van Spronsen gave it [van Spronsen 1969, p. 220]: 'That the element next to calcium later proved to be scandium, was fortuitous; Mendeleev cannot be said to have already foreseen this element in 1869.'

[11]The elements placed in the last four rows of the table puzzled Mendeleev, as is apparent from the glut of question marks and the fact that several are out of order according to their assigned atomic weights. Many of these elements were rare and poorly characterized at the time. Didymium appeared in many lists of elements at this time, but it was later proved to consist of two elements, praseodymium and neodymium. The atomic weights of erbium, yttrium (standard symbol Y), indium, cerium, lanthanum, and thorium are wrong. The interdependence of atomic weights and chemical formulas that plagued determinations of atomic weight since the time of Dalton was still problematic for these elements. Most of them elements (erbium, yttrium, cerium, lanthanum, and the component elements of didymium) belong to the family of rare earths, a group whose classification would present problems for many years to come. (Thorium belongs to the group of elements immediately below most of the rare earths.) Many of the rare earths were not yet discovered, and (as already noted) the atomic weights of the known elements were not well determined. The chemical properties of the rare earths are so similar that they were difficult to distinguish and to separate. Mendeleev made some progress with these elements in the next couple of years. His 1871 table [Mendeleev 1871] has correct weights for yttrium, indium, cerium, and thorium, and correct classification for yttrium and indium.

[12]Translator's note: In his 1889 Faraday lecture [Mendeleev 1889], Mendeleev used the word 'periodicity' rather than the phrase 'stepwise variation' in translating this sentence from his 1869 paper. 'Periodicity' is certainly an appropriate term to describe the cyclic repetition in properties evident in this arrangement. It is worth noting, however, that the German words read in 1869 by Western European scientists (stufenweise Abänderung) lack the implication of repetition inherent in the term periodicity. --CJG

[13]Groups of similar elements with consecutive atomic weights are a little-emphasized part of classification systems from Mendeleev's time and before (cf. Newlands 1864) to the present.

[14]The existence of a very regular progression in atomic weight among elements with similar chemical behavior had attracted the attention of chemists almost from the time they began to measure atomic weights [Döbereiner 1829]. The triad of elements Mendeleev cites here includes two (rubidium and cesium) discovered in the early 1860s. Mendeleev's table, however, goes beyond strictly regular isolated triads of elements to a systematic classification (albeit not always correct) of all known elements.

[15]The valence of an element is essentially the number of bonds that element can make when it forms compounds with other elements. An atom of hydrogen, for example, can make just one bond, so its valence is one; we call it monovalent. An atom of oxygen can bond with two atoms of hydrogen, so its valence is two. Some elements, particularly heavier elements, have more than one characteristic valence. (For example, lead has valence 2 and 4; thallium has valence 1 and 3. See note 4 above.) The elements in the cited series have valences 1, 2, 3, 4, 3, 2, and 1 respectively.

[16]Mendeleev is correct in this observation. The two lightest elements, hydrogen and helium (the latter as yet unknown) are the most common elements in the universe, making up the bulk of stars. Oxygen and silicon are the most common elements in the earth's crust. Iron is the heaviest element among the most abundant elements in the stars and the earth's crust.

[17]Although the chemical behavior of elements in the same family is similar, it is not identical: there are differences due to the difference in atomic weight. For example, both chlorine and iodine form compounds with one atom of hydrogen: HCl and HI. These compounds are similar, in that they are both corrosive gases which dissolve readily in water. But they differ in that HI has, for example, a higher boiling point and melting point than HCl (typical of the heavier of a pair of related compounds).

[18]In later publications [Mendeleev 1871] Mendeleev went into considerable detail regarding the properties of predicted elements. The success of these predictions played a part in establishing the periodic system, although apparently not the primary part. [Brush 1996] See Scerri & Worrall 2001 for a discussion of prediction and accommodation in the periodic table.

[19]Mendeleev went on to incorporate this 'correction' in his 1871 table [Mendeleev 1871], listing the atomic weight of tellurium as 125. But the 'correction' is erroneous. Mendeleev was right to put tellurium in the same group with sulfur and oxygen; however, strict order of atomic weights according to the best information he had available would have required iodine (127) to come before tellurium (128). He was suspicious of this apparent inversion of atomic weight order; as it happens, the atomic weights Mendeleev had available to him agree with the currently accepted values.

While his suggestion to change that of tellurium was wrong, his classification was correct and his faith in the regularity of the periodic system was only slightly misplaced. The natural order of the elements is not quite one of increasing atomic weight, but one of increasing atomic number. In 1913, a discovery by Henry Moseley made the atomic number more than simply a rank order for the elements [Moseley 1913, 1914]. The atomic number is the same as the quantity of positive charge in the nucleus of an atom. The periodic system contains a few 'inversions' of atomic weight, but no inversions of atomic number.

References

• Stephen G. Brush, 'The Reception of Mendeleev's Periodic Law in America and Britain,' Isis87 595-628 (1996)
• Johann Döbereiner, Poggendorf's Annalen der Physik und Chemie15, 301-307 (1829); translated as 'An Attempt to Group Elementary Substances according to Their Analogies,' in Henry M. Leicester & Herbert S. Klickstein, eds., A Source Book in Chemistry, 1400-1900 (Cambridge, MA: Harvard, 1952)], pp. 268-272.
• Henry M. Leicester, 'Factors Which Led Mendeleev to the Periodic Law,' Chymia1, 67-74 (1948)
• Paul Émile Lecoq de Boisbaudran, 'About a New Metal, Gallium,' Annales de Chimie10, 100-141 (1877)
• Dmitrii Mendeleev, 'On the Relationship of the Properties of the Elements to their Atomic Weights,' Zhurnal Russkoe Fiziko-Khimicheskoe Obshchestvo1, 60-77 (1869); abstracted in Zeitschrift für Chemie12, 405-406 (1869); abstract translated and annotated above
• Dmitrii Mendeleev, Zhurnal Russkoe Fiziko-Khimicheskoe Obshchestvo3, 25 (1871); German version, 'Die periodische Gesetzmässigkeit der chemischen Elemente,' Annalen der Chemie und Pharmacie Supplement 8, 133-229 (1872); table from this paper
• Dmitrii Mendeleev, 'The Periodic Law of the Chemical Elements,' Journal of the Chemical Society (London)55, 634-656 (1889); annotated text.
• B. N. Menschutkin, 'Early History of Mendeléeff's Periodic Law,' Nature133, 946 (1934)
• Henry G. J. Moseley, 'The High Frequency Spectra of the Elements,' Philosophical Magazine26, 1024-1034 (1913); 27, 703-713 (1914)
• John A. R. Newlands, 'On Relations Among the Equivalents,' Chemical News10, 94-95 (1864); annotated text
• Lars Fredrick Nilson, 'About Ytterbine, the New Earth of Marignac,' Comptes Rendus88, 642-664 (1879)
• Eric R. Scerri & John Worrall, 'Prediction and the Periodic Table,' Studies in History and Philosophy of Science32, 407-452 (2001)
• J. W. van Spronsen, The Periodic System of Chemical Elements: a History of the First Hundred Years (Amsterdam: Elsevier, 1969)
• Clemens Winkler, 'Germanium, Ge, a New Nonmetallic Element,' Berichte der Deutschen Chemischen Gesellschaft 19, 210-211 (1886)

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1.6 Isotopes and Atomic Masses

Learning Objective

1. To know the meaning of isotopes and atomic masses.

Rutherford’s nuclear model of the atom helped explain why atoms of different elements exhibit different chemical behavior. The identity of an element is defined by its atomic number (Z)The number of protons in the nucleus of an atom of an element., the number of protons in the nucleus of an atom of the element. The atomic number is therefore different for each element. The known elements are arranged in order of increasing Z in the periodic tableA chart of the chemical elements arranged in rows of increasing atomic number so that the elements in each column (group) have similar chemical properties. (Figure 1.24 'The Periodic Table Showing the Elements in Order of Increasing '; also see Chapter 32 'Appendix H: Periodic Table of Elements'),We will explain the rationale for the peculiar format of the periodic table in Chapter 7 'The Periodic Table and Periodic Trends'. in which each element is assigned a unique one-, two-, or three-letter symbol. The names of the elements are listed in the periodic table, along with their symbols, atomic numbers, and atomic masses. The chemistry of each element is determined by its number of protons and electrons. In a neutral atom, the number of electrons equals the number of protons.

Atomic Mass Of First 50 Elements Found

Figure 1.24 The Periodic Table Showing the Elements in Order of Increasing Z

As described in Section 1.7 'Introduction to the Periodic Table', the metals are on the bottom left in the periodic table, and the nonmetals are at the top right. The semimetals lie along a diagonal line separating the metals and nonmetals.

In most cases, the symbols for the elements are derived directly from each element’s name, such as C for carbon, U for uranium, Ca for calcium, and Po for polonium. Elements have also been named for their properties [such as radium (Ra) for its radioactivity], for the native country of the scientist(s) who discovered them [polonium (Po) for Poland], for eminent scientists [curium (Cm) for the Curies], for gods and goddesses [selenium (Se) for the Greek goddess of the moon, Selene], and for other poetic or historical reasons. Some of the symbols used for elements that have been known since antiquity are derived from historical names that are no longer in use; only the symbols remain to remind us of their origin. Examples are Fe for iron, from the Latin ferrum; Na for sodium, from the Latin natrium; and W for tungsten, from the German wolfram. Examples are in Table 1.4 'Element Symbols Based on Names No Longer in Use'. As you work through this text, you will encounter the names and symbols of the elements repeatedly, and much as you become familiar with characters in a play or a film, their names and symbols will become familiar.

Table 1.4 Element Symbols Based on Names No Longer in Use

Element	Symbol	Derivation	Meaning
antimony	Sb	stibium	Latin for “mark”
copper	Cu	cuprum	from Cyprium, Latin name for the island of Cyprus, the major source of copper ore in the Roman Empire
gold	Au	aurum	Latin for “gold”
iron	Fe	ferrum	Latin for “iron”
lead	Pb	plumbum	Latin for “heavy”
mercury	Hg	hydrargyrum	Latin for “liquid silver”
potassium	K	kalium	from the Arabic al-qili, “alkali”
silver	Ag	argentum	Latin for “silver”
sodium	Na	natrium	Latin for “sodium”
tin	Sn	stannum	Latin for “tin”
tungsten	W	wolfram	German for “wolf stone” because it interfered with the smelting of tin and was thought to devour the tin

Recall from Section 1.5 'The Atom' that the nuclei of most atoms contain neutrons as well as protons. Unlike protons, the number of neutrons is not absolutely fixed for most elements. Atoms that have the same number of protons, and hence the same atomic number, but different numbers of neutrons are called isotopesAtoms that have the same numbers of protons but different numbers of neutrons.. All isotopes of an element have the same number of protons and electrons, which means they exhibit the same chemistry. The isotopes of an element differ only in their atomic mass, which is given by the mass number (A)The number of protons and neutrons in the nucleus of an atom of an element., the sum of the numbers of protons and neutrons.

The element carbon (C) has an atomic number of 6, which means that all neutral carbon atoms contain 6 protons and 6 electrons. In a typical sample of carbon-containing material, 98.89% of the carbon atoms also contain 6 neutrons, so each has a mass number of 12. An isotope of any element can be uniquely represented as $\text{X}_Z^A\text{,}$ where X is the atomic symbol of the element. The isotope of carbon that has 6 neutrons is therefore $\text{C}_6^{\text{12}}\text{.}$ The subscript indicating the atomic number is actually redundant because the atomic symbol already uniquely specifies Z. Consequently, $\text{C}_6^{\text{12}}$ is more often written as ¹²C, which is read as “carbon-12.” Nevertheless, the value of Z is commonly included in the notation for nuclear reactions because these reactions involve changes in Z, as described in Chapter 20 'Nuclear Chemistry'.

In addition to ¹²C, a typical sample of carbon contains 1.11% $\text{C}_6^{\text{13}}$ (¹³C), with 7 neutrons and 6 protons, and a trace of $\text{C}_6^{\text{14}}$ (¹⁴C), with 8 neutrons and 6 protons. The nucleus of ¹⁴C is not stable, however, but undergoes a slow radioactive decay that is the basis of the carbon-14 dating technique used in archaeology (see Chapter 14 'Chemical Kinetics'). Many elements other than carbon have more than one stable isotope; tin, for example, has 10 isotopes. The properties of some common isotopes are in Table 1.5 'Properties of Selected Isotopes'.

Table 1.5 Properties of Selected Isotopes

Element	Symbol	Atomic Mass (amu)	Isotope Mass Number	Isotope Masses (amu)	Percent Abundances (%)
hydrogen	H	1.0079	1	1.007825	99.9855
			2	2.014102	0.0115
boron	B	10.81	10	10.012937	19.91
			11	11.009305	80.09
carbon	C	12.011	12	12 (defined)	99.89
			13	13.003355	1.11
oxygen	O	15.9994	16	15.994915	99.757
			17	16.999132	0.0378
			18	17.999161	0.205
iron	Fe	55.845	54	53.939611	5.82
			56	55.934938	91.66
			57	56.935394	2.19
			58	57.933276	0.33
uranium	U	238.03	234	234.040952	0.0054
			235	235.043930	0.7204
			238	238.050788	99.274

Sources of isotope data: G. Audi et al., Nuclear Physics A 729 (2003): 337–676; J. C. Kotz and K. F. Purcell, Chemistry and Chemical Reactivity, 2nd ed., 1991.

Example 5

An element with three stable isotopes has 82 protons. The separate isotopes contain 124, 125, and 126 neutrons. Identify the element and write symbols for the isotopes.

Given: number of protons and neutrons

Asked for: element and atomic symbol

Strategy:

A Refer to the periodic table (see Chapter 32 'Appendix H: Periodic Table of Elements') and use the number of protons to identify the element.

B Calculate the mass number of each isotope by adding together the numbers of protons and neutrons.

C Give the symbol of each isotope with the mass number as the superscript and the number of protons as the subscript, both written to the left of the symbol of the element.

Solution:

A The element with 82 protons (atomic number of 82) is lead: Pb.

B For the first isotope, A = 82 protons + 124 neutrons = 206. Similarly, A = 82 + 125 = 207 and A = 82 + 126 = 208 for the second and third isotopes, respectively. The symbols for these isotopes are $\text{P}_{82}^{206}\text{b},$$\text{P}_{82}^{207}\text{b,}$ and $\text{P}_{82}^{208}\text{b,}$ which are usually abbreviated as ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb.

Exercise

Identify the element with 35 protons and write the symbols for its isotopes with 44 and 46 neutrons.

Answer: $\text{B}_{35}^{79}\text{r}$ and $\text{B}_{35}^{81}\text{r}$ or, more commonly, ⁷⁹Br and ⁸¹Br.

Although the masses of the electron, the proton, and the neutron are known to a high degree of precision (Table 1.3 'Properties of Subatomic Particles*'), the mass of any given atom is not simply the sum of the masses of its electrons, protons, and neutrons. For example, the ratio of the masses of ¹H (hydrogen) and ²H (deuterium) is actually 0.500384, rather than 0.49979 as predicted from the numbers of neutrons and protons present. Although the difference in mass is small, it is extremely important because it is the source of the huge amounts of energy released in nuclear reactions (Chapter 20 'Nuclear Chemistry').

Because atoms are much too small to measure individually and do not have a charge, there is no convenient way to accurately measure absolute atomic masses. Scientists can measure relative atomic masses very accurately, however, using an instrument called a mass spectrometer. The technique is conceptually similar to the one Thomson used to determine the mass-to-charge ratio of the electron. First, electrons are removed from or added to atoms or molecules, thus producing charged particles called ionsA charged particle produced when one or more electrons is removed from or added to an atom or molecule.. When an electric field is applied, the ions are accelerated into a separate chamber where they are deflected from their initial trajectory by a magnetic field, like the electrons in Thomson’s experiment. The extent of the deflection depends on the mass-to-charge ratio of the ion. By measuring the relative deflection of ions that have the same charge, scientists can determine their relative masses (Figure 1.25 'Determining Relative Atomic Masses Using a Mass Spectrometer'). Thus it is not possible to calculate absolute atomic masses accurately by simply adding together the masses of the electrons, the protons, and the neutrons, and absolute atomic masses cannot be measured, but relative masses can be measured very accurately. It is actually rather common in chemistry to encounter a quantity whose magnitude can be measured only relative to some other quantity, rather than absolutely. We will encounter many other examples later in this text. In such cases, chemists usually define a standard by arbitrarily assigning a numerical value to one of the quantities, which allows them to calculate numerical values for the rest.

Figure 1.25 Determining Relative Atomic Masses Using a Mass Spectrometer

Chlorine consists of two isotopes, ³⁵Cl and ³⁷Cl, in approximately a 3:1 ratio. (a) When a sample of elemental chlorine is injected into the mass spectrometer, electrical energy is used to dissociate the Cl₂ molecules into chlorine atoms and convert the chlorine atoms to Cl⁺ ions. The ions are then accelerated into a magnetic field. The extent to which the ions are deflected by the magnetic field depends on their relative mass-to-charge ratios. Note that the lighter ³⁵Cl⁺ ions are deflected more than the heavier ³⁷Cl⁺ ions. By measuring the relative deflections of the ions, chemists can determine their mass-to-charge ratios and thus their masses. (b) Each peak in the mass spectrum corresponds to an ion with a particular mass-to-charge ratio. The abundance of the two isotopes can be determined from the heights of the peaks.

The arbitrary standard that has been established for describing atomic mass is the atomic mass unit (amu)One-twelfth of the mass of one atom of $\text{C}_{\text{12}}$; $\text{1 amu}=\text{1}.\text{66}\times \text{1}{0}^{-\text{24}}\text{g}$., defined as one-twelfth of the mass of one atom of ¹²C. Because the masses of all other atoms are calculated relative to the ¹²C standard, ¹²C is the only atom listed in Table 1.5 'Properties of Selected Isotopes' whose exact atomic mass is equal to the mass number. Experiments have shown that 1 amu = 1.66 × 10⁻²⁴ g.

Mass spectrometric experiments give a value of 0.167842 for the ratio of the mass of ²H to the mass of ¹²C, so the absolute mass of ²H is

$$\frac{\text{mass of}\text{H}_{\text{2}}}{\cancel{\text{mass of}\text{C}_{\text{12}}}}\times \cancel{\text{mass of}\text{C}_{\text{12}}}=\text{0}\text{.167842}\times \text{12 amu}=\text{2}\text{.104104 amu}$$

The masses of the other elements are determined in a similar way.

The periodic table (see Chapter 32 'Appendix H: Periodic Table of Elements') lists the atomic masses of all the elements. If you compare these values with those given for some of the isotopes in Table 1.5 'Properties of Selected Isotopes', you can see that the atomic masses given in the periodic table never correspond exactly to those of any of the isotopes. Because most elements exist as mixtures of several stable isotopes, the atomic mass of an element is defined as the weighted average of the masses of the isotopes. For example, naturally occurring carbon is largely a mixture of two isotopes: 98.89% ¹²C (mass = 12 amu by definition) and 1.11% ¹³C (mass = 13.003355 amu). The percent abundance of ¹⁴C is so low that it can be ignored in this calculation. The average atomic mass of carbon is then calculated as

(0.9889 × 12 amu) + (0.0111 × 13.003355 amu) = 12.01 amu

Carbon is predominantly ¹²C, so its average atomic mass should be close to 12 amu, which is in agreement with our calculation.

The value of 12.01 is shown under the symbol for C in the periodic table (see Chapter 32 'Appendix H: Periodic Table of Elements'), although without the abbreviation amu, which is customarily omitted. Thus the tabulated atomic mass of carbon or any other element is the weighted average of the masses of the naturally occurring isotopes.

Example 6

Naturally occurring bromine consists of the two isotopes listed in the following table:

Isotope	Exact Mass (amu)	Percent Abundance (%)
79Br	78.9183	50.69
81Br	80.9163	49.31

Calculate the atomic mass of bromine.

Given: exact mass and percent abundance

Asked for: atomic mass

Strategy:

A Convert the percent abundances to decimal form to obtain the mass fraction of each isotope.

B Multiply the exact mass of each isotope by its corresponding mass fraction (percent abundance ÷ 100) to obtain its weighted mass.

C Add together the weighted masses to obtain the atomic mass of the element.

D Check to make sure that your answer makes sense.

Solution:

A The atomic mass is the weighted average of the masses of the isotopes. In general, we can write

atomic mass of element = [(mass of isotope 1 in amu) (mass fraction of isotope 1)] + [(mass of isotope 2) (mass fraction of isotope 2)] + …

Bromine has only two isotopes. Converting the percent abundances to mass fractions gives

$$\begin{array}{l}\text{B}_{79}\text{r:}\frac{50.69}{100}=0.5069\\ \text{B}_{81}\text{r:}\frac{49.31}{100}=0.4931\end{array}$$

B Multiplying the exact mass of each isotope by the corresponding mass fraction gives the isotope’s weighted mass:

⁷⁹Br: 79.9183 amu × 0.5069 = 40.00 amu⁸¹Br: 80.9163 amu × 0.4931 = 39.90 amu

C The sum of the weighted masses is the atomic mass of bromine is

40.00 amu + 39.90 amu = 79.90 amu

D This value is about halfway between the masses of the two isotopes, which is expected because the percent abundance of each is approximately 50%.

- Atomic Number

Exercise

Magnesium has the three isotopes listed in the following table:

Isotope	Exact Mass (amu)	Percent Abundance (%)
24Mg	23.98504	78.70
25Mg	24.98584	10.13
26Mg	25.98259	11.17

Use these data to calculate the atomic mass of magnesium.

Answer: 24.31 amu

Summary

Each atom of an element contains the same number of protons, which is the atomic number (Z). Neutral atoms have the same number of electrons and protons. Atoms of an element that contain different numbers of neutrons are called isotopes. Each isotope of a given element has the same atomic number but a different mass number (A), which is the sum of the numbers of protons and neutrons. Minecraft lite shaders for mac. The relative masses of atoms are reported using the atomic mass unit (amu), which is defined as one-twelfth of the mass of one atom of carbon-12, with 6 protons, 6 neutrons, and 6 electrons. The atomic mass of an element is the weighted average of the masses of the naturally occurring isotopes. When one or more electrons are added to or removed from an atom or molecule, a charged particle called an ion is produced, whose charge is indicated by a superscript after the symbol.

Key Takeaway

• The mass of an atom is a weighted average that is largely determined by the number of its protons and neutrons, whereas the number of protons and electrons determines its charge.

Conceptual Problems

1. Complete the following table for the missing elements, symbols, and numbers of electrons.

   Element	Symbol	Number of Electrons
   molybdenum
   19
   titanium
   B
   53
   Sm
   helium
   14

2. Complete the following table for the missing elements, symbols, and numbers of electrons.

   Element	Symbol	Number of Electrons
   lanthanum
   Ir
   aluminum
   80
   sodium
   Si
   9
   Be

3. Is the mass of an ion the same as the mass of its parent atom? Explain your answer.

4. What isotopic standard is used for determining the mass of an atom?

5. Give the symbol $\text{X}_Z^A$ for these elements, all of which exist as a single isotope.

   1. beryllium
   2. ruthenium
   3. phosphorus
   4. aluminum
   5. cesium
   6. praseodymium
   7. cobalt
   8. yttrium
   9. arsenic

6. Give the symbol $\text{X}_Z^A$ for these elements, all of which exist as a single isotope.

   1. fluorine
   2. helium
   3. terbium
   4. iodine
   5. gold
   6. scandium
   7. sodium
   8. niobium
   9. manganese

7. Identify each element, represented by X, that have the given symbols.

   1. $\text{X}_{26}^{55}$
   2. $\text{X}_{33}^{74}$
   3. $\text{X}_{12}^{24}$
   4. $\text{X}_{53}^{127}$
   5. $\text{X}_{18}^{40}$
   6. $\text{X}_{63}^{152}$

Numerical Problems

Helium

Please be sure you are familiar with the topics discussed in Essential Skills 1 (Section 1.9 'Essential Skills 1') before proceeding to the Numerical Problems.

1. The isotopes ¹³¹I and ⁶⁰Co are commonly used in medicine. Determine the number of neutrons, protons, and electrons in a neutral atom of each.

2. Determine the number of protons, neutrons, and electrons in a neutral atom of each isotope:

   1. ⁹⁷Tc
   2. ¹¹³In
   3. ⁶³Ni
   4. ⁵⁵Fe

3. Both technetium-97 and americium-240 are produced in nuclear reactors. Determine the number of protons, neutrons, and electrons in the neutral atoms of each.

4. The following isotopes are important in archaeological research. How many protons, neutrons, and electrons does a neutral atom of each contain?

   1. ²⁰⁷Pb
   2. ¹⁶O
   3. ⁴⁰K
   4. ¹³⁷Cs
   5. ⁴⁰Ar

5. Copper, an excellent conductor of heat, has two isotopes: ⁶³Cu and ⁶⁵Cu. Use the following information to calculate the average atomic mass of copper:

   Isotope	Percent Abundance (%)	Atomic Mass (amu)
   63Cu	69.09	62.9298
   65Cu	30.92	64.9278

6. Silicon consists of three isotopes with the following percent abundances:

   Isotope	Percent Abundance (%)	Atomic Mass (amu)
   28Si	92.18	27.976926
   29Si	4.71	28.976495
   30Si	3.12	29.973770

   Calculate the average atomic mass of silicon.

7. Complete the following table for neon. The average atomic mass of neon is 20.1797 amu.

   Isotope	Percent Abundance (%)	Atomic Mass (amu)
   20Ne	90.92	19.99244
   21Ne	0.257	20.99395
   22Ne

8. Are $\text{X}_{28}^{63}$ and $\text{X}_{29}^{62}$ isotopes of the same element? Explain your answer.

9. Complete the following table:

   Isotope	Number of Protons	Number of Neutrons	Number of Electrons
   238X	95
   238U
   75	112

10. Complete the following table:

    Isotope	Number of Protons	Number of Neutrons	Number of Electrons
    57Fe
    40X	20
    36S

11. Using a mass spectrometer, a scientist determined the percent abundances of the isotopes of sulfur to be 95.27% for ³²S, 0.51% for ³³S, and 4.22% for ³⁴S. Use the atomic mass of sulfur from the periodic table (see Chapter 32 'Appendix H: Periodic Table of Elements') and the following atomic masses to determine whether these data are accurate, assuming that these are the only isotopes of sulfur: 31.972071 amu for ³²S, 32.971459 amu for ³³S, and 33.967867 amu for ³⁴S.

12. The percent abundances of two of the three isotopes of oxygen are 99.76% for ¹⁶O, and 0.204% for ¹⁸O. Use the atomic mass of oxygen given in the periodic table (see Chapter 32 'Appendix H: Periodic Table of Elements') and the following data to determine the mass of ¹⁷O: 15.994915 amu for ¹⁶O and 17.999160 amu for ¹⁸O.

13. Which element has the higher proportion by mass in NaI?

14. Which element has the higher proportion by mass in KBr?