Masses, atomic

PRACTICE EXAMPLE B An isotope with atomic number 64 and mass number 158 is found to have a mass ratio relative to that of carbon-12 of 13.16034. What is the isotope, what is its atomic mass in u, and what is its mass relative to oxygen-16  

The amount of carbon-14 on Earth is too small to affect the atomic mass of carbon. 

The first term on the right side of equation (2.3) represents the contribution from isotope 1 the second term represents the contribution from isotope 2  

We will use equation (2.3), with appropriate data, in Example 2-6, but first let us illustrate the ideas of fractional abundance and a weighted average in a different way in establishing the atomic mass of carbon. The mass spectrum of a particular sample of carbon shows that 98.93% of the carbon atoms are carbon-12 with a mass of exactly 12 u the rest are carbon-13 atoms with a mass of 13.0033548378 u. Therefore  

It is important to note that, in the setup just shown, 12 u and the 1 appearing in the factor (1 — 0.9893) are exact niunbers. Thus, by applying the rules for significant figures (see Chapter 1), the atomic mass of carbon can be reported with four decimal places. 

Section 3.4 describes a method for determining atomic mass. 

One atomic mass unit is also called one dalton. 

In this chapter, we will use what we have learned about chemical structure and formulas in studying the mass relationships of atoms and molecules. These relationships in turn will help us to explain the composition of compounds and the ways in which composition changes. 

The mass of an atom depends on the number of electrons, protons, and neutrons it contains. Knowledge of an atom s mass is important in laboratory work. But atoms are extremely small particles—even the smallest speck of dust that our unaided eyes can detect contains as many as 1 X 10 atoms Clearly we cannot weigh a single atom, but it is possible to determine the mass of one atom relative to another experimentally. The first step is to assign a value to the mass of one atom of a given element so that it can be used as a standard. 

When you look up the atomic mass of carbon in a table such as the one on the inside front cover of this book, you will find that its value is not 12.00 amu but 12.01 amu. The reason for the difference is that most naturally occurring elements (including carbon) have more than one isotope. This means that when we measure the atomic mass of an element, we must generally settle for the average mass of the naturally occurring mixture of isotopes. For example, the natural abundances of carbon-12 and carbon-13 are 98.90 percent and 1.10 percent, respectively. The atomic mass of carbon-13 has been determined to be 13.00335 amn. Thus, the average atomic mass of carbon can be calculated as follows  

Note The accepted SI unit for mass is the kilogram (kg). SI is from French meaning Le Systeme International d unites. However, as the mass of an atom, ion, or molecule is significantly less than the standard SI unit, specific mass units needed to be introduced. That accepted by the SI is the Dalton (Da). More commonly used, however, is the numerically equivalent unified atomic mass unit (u). Before 1961, the term atomic mass unit (amu) was also in use. 1 Da equates to 1.6605 X 10-27 kg. 

Also of note is the fact that the mass of an isotope is not exactly equal to the Slim of the masses of the protons and neutrons within the nucleus of the respective atom (electrons are not considered as their masses are a small fraction of the proton/neutron s masses). Rest masses of free protons, neutrons, and electrons are listed along with their mass in unified atomic mass units and their charge in units of coulombs in Table 2.1. 

As an example, the mass of the He isotope is 4.0026 u, whereas the sum of the rest masses of free proton and neutrons (see Table 2.1) is 4.0320 u. This loss of mass arises from the fact that energy is required to overcome the electromagnetic repulsion experienced as two or more protons brought in close vicinity to each odier. This energy is attained at the expense of mass consistent with the equation E = mc where c is the speed of light (this is the basis of how fusion reactors derive energy). 

As a result of this electromagnetic repulsion and the fact that all masses are scaled (1 Da equates to l/12th the mass of the isotope), isotopes with masses lesser or greater than display a mass that diverges slightly from the atomic mass number (A). Recall A equates to the sum of protons and neutrons within the 

TABLE 2.1 Rest Mass and Charge of Free (Unbound) Ground State Protons, Neutrons, and Electrons. 

Scientists are learning to use isotopes to determine the origin of drugs and gems. It turns out that isotope ratios similar to those used in carbon dating can also identify the source of cocaine or the birthplace of emeralds. 

It turns out that a similar isotopic analysis of oxygen has led researchers in France to be able to track the birthplace of emeralds. Very high quality emeralds have few inclusions (microscopic cavities). Gemologists use these 

The mass of a single atom is far too small to measure on a balance, but fairly precise determinations of the masses of individual atoms can be made with an instrument called a mass spectrometer. The mass of a single hydrogen atom is 1.673 X 10 g. 

However, it is neither convenient nor practical to compare the actual masses of atoms expressed in grams therefore, a table of relative atomic masses using atomic mass units was devised. (The term atomic weight is sometimes used instead of atomic mass.) The carbon isotope having six protons and six neutrons and designated carbon-12, or gC, was chosen as the standard for atomic masses. This reference isotope was assigned a value of exactly 12 atomic mass units (amu). Thus, 1 atomic mass unit is defined as equal to exactly 1/12 of the mass of a carbon-12 atom. The actual mass of a carbon-12 atom is 1.9927 x 10 g, and that of one atomic mass unit is 1.6606 x 10 g. 1 amu = 1.6606 x I0 g 

In the table of atomic masses, all elements then have values that are relative to the mass assigned to the reference isotope, carbon-12. 

Identify the true statements, and rewrite the false statements to make them true. 

Co to http //now.brookscole.com/ cracoliceSe and click Coached Problems for a step-by-step tutorial on Writing Atomic Symbols. 

8 Given the relative abundances of the natural isotopes of an element and the atomic mass of each isotope, calculate the atomic mass of the element. 

The mass of an atom is very small—much too small to be measured on a balance. Nevertheless, early chemists did find ways to isolate samples of elements that contained the same number of atoms. These samples were weighed and compared. The ratio of the masses of equal numbers of atoms of different elements is the same as the ratio of the masses of individual atoms. From this, a scale of relative atomic masses was developed. Chemists didn t know about isotopes at that time, so they applied the idea of what was then called atomic weight to all of the natural isotopes of an element. 

Today we recognize that a sample of a pure element contains atoms that have different masses. By worldwide agreement, the masses of atoms are expressed in atomic mass units (amu), which are exactly V12 the mass of a carbon-12 atom  

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Either choice is invariant to pemuitation of the atom masses. 

We now compare the results calculated for the fundamental frequency of the symmetric stretching mode with the only available experimental datum [78] of 326 cm . The theoretical result is seen to exceed experiment by only 8.3%. It should be recalled that the Li3 and Li3 tiimers have for lowest J the values 0 and respectively. Thus, the istopic species Li3 cannot contribute to the nuclear spin weight in Eq. (64), since the calculations for half-integer J should employ different nuclear spin weights. Note that atomic masses have been used... 

The location of the crossing seam (or seam) for an X3 system is established from the requirement that /-ab = rec = r c, where j-ab, rec, and fAc are the interatomic distances. Since the goal are the the geometric properties produced by this seam, hyperspherical coordinates (p,0,[Pg.608]

By 1850. values of atomic weights (now called relative atomic masses) had been ascertained for many elements, and a knowledge of these enabled Newlands in 1864 to postulate a law of octaves. When the elements were arranged in order ol increasing atomic weight, each... 

All Group IV elements form both a monoxide, MO, and a dioxide, MO2. The stability of the monoxide increases with atomic weight of the Group IV elements from silicon to lead, and lead(II) oxide, PbO, is the most stable oxide of lead. The monoxide becomes more basic as the atomic mass of the Group IV elements increases, but no oxide in this Group is truly basic and even lead(II) oxide is amphoteric. Carbon monoxide has unusual properties and emphasises the different properties of the group head element and its compounds. 

The change from non-metallic to metallic properties of the Group V elements as the atomic mass of the element increases is shown in their reactions with alkalis. 

The matrix M contains atomic masses on its diagonal, and the Hessian matrix F contains the second derivatives of the potential energy evaluated at Xq. 

To facilitate conformational transitions in the before-mentioned adenylate kinase, Elamrani and co-workers scaled all atomic masses by a large factor thus allowing the use of a high effective simulation temperature of 2000K ([Elamrani et al. 1996]). To prevent protein unfolding, elements of secondary structure had to be constrained. 

The function/( C) may have a very simple form, as is the case for the calculation of the molecular weight from the relative atomic masses. In most cases, however,/( Cj will be very complicated when it comes to describe the structure by quantum mechanical means and the property may be derived directly from the wavefunction for example, the dipole moment may be obtained by applying the dipole operator. 

Natural titanium consists of five isotopes with atomic masses from 46 to 50. All are stable. Eight other unstable isotopes are known. 

Thirty isotopes of tellurium are known, with atomic masses ranging from 108 to 137. Natural tellurium consists of eight isotopes. 

When freshly exposed to air, thallium exhibits a metallic luster, but soon develops a bluish-gray tinge, resembling lead in appearance. A heavy oxide builds up on thallium if left in air, and in the presence of water the hydride is formed. The metal is very soft and malleable. It can be cut with a knife. Twenty five isotopic forms of thallium, with atomic masses ranging from 184 to 210 are recognized. Natural thallium is a mixture of two isotopes. A mercury-thallium alloy, which forms a eutectic at 8.5% thallium, is reported to freeze at -60C, some 20 degrees below the freezing point of mercury. 

Twenty five isotopes of polonium are known, with atomic masses ranging from 194 to 218. Polonium-210 is the most readily available. Isotopes of mass 209 (half-life 103 years) and mass 208 (half-life 2.9 years) can be prepared by alpha, proton, or deuteron bombardment of lead or bismuth in a cyclotron, but these are expensive to produce. 

February 9,1996 at 10 37 pm, at the Gesellschaft fur Schwerionenforschung in Darmstadt, Germany a team of scientists discovered their sixth element. This element has the atomic number 112 and is currently the heaviest element ever produced by man. It has an atomic mass of 277. 

Searches for the element on earth have been fruitless, and it now appears that promethium is completely missing from the earth s crust. Promethium, however, has been identified in the spectrum of the star HR465 in Andromeda. This element is being formed recently near the star s surface, for no known isotope of promethium has a half-life longer than 17.7 years. Seventeen isotopes of promethium, with atomic masses from 134 to 155 are now known. Promethium-147, with a half-life of 2.6 years, is the most generally useful. Promethium-145 is the longest lived, and has a specific activity of 940 Ci/g. 

Terbium is reasonably stable in air. It is a silver-gray metal, and is malleable, ductile, and soft enough to be cut with a knife. Two crystal modifications exist, with a transformation temperature of 1289oC. Twenty one isotopes with atomic masses ranging from 145 to 165 are recognized. The oxide is a chocolate or dark maroon color. 

The periodic table is the most important chemistry reference there is. It arranges all the known elements in an informative array. Elements are arranged left to right and top to bottom in order of increasing atomic number.. This order generally coincides with increasing atomic mass... 

Using the data in the table scientists, students, and others that are familiar with the periodic table can extract infomiation conceming individual elements. For instance, a scientist can use carbon s atomic mass mass to detemiine how many carbon atoms there are in a 1 kilogram block of carbon. 

The atomic mass is the average mass of an element in atomic mass units ("amu"). 

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