Relative scale of atomic masses

In Chapter 4, you learned that the relative scale of atomic masses uses the isotope carbon-12 as the standard. Each atom of carbon-12 has a mass of 12 atomic mass units (amu). The atomic masses of all other elements are established relative to carbon-12. For example, an atom of hydrogen-1 has a mass of 1 amu. The mass of an atom of helium-4 is 4 amu. Therefore, the mass of one atom of hydrogen-1 is one-twelfth the mass of one atom of carbon-12. The mass of one atom of helium-4 is one-third the mass of one atom of carbon-12. 

As the chemists of the eighteenth and nineteenth centuries painstakingly sought information about the compositions of compounds and tried to systematize their knowledge, it became apparent that each element has a characteristic mass relative to every other element. Although these early scientists did not have the experimental means to measure the mass of each kind of atom, they succeeded in defining a relative scale of atomic masses. 

Masses of atoms expressed in grams are very small. As we shall see, an atom of oxygen-16, for example, has a mass of 2.656 x 10 g. For most chemical calculations it is more convenient to use relative atomic masses. As you learned when you studied scientific measurement, scientists use standards of measurement that are constant and are the same everywhere. In order to set up a relative scale of atomic mass, one atom has been arbitrarily chosen as the standard and assigned a mass value. The masses of all other atoms are expressed in relation to this standard. 

A relative scale of atomic weights (as the weighted average of all forms, or isotopes, of a particular element found in nature) has been developed. The base of this scale is the assignment of a mass of 12.0000 to the isotope of carbon containing 5 protons, 5 neutrons, and 6 electrons. An atomic weight table can be found in Table 2.2. 

Atoms are so tiny that, until recently, the masses of individual atoms could not be measured directly (Figure 3.7). However, because mass was so important in Dalton s theory, some measure of atomic masses was necessary. Therefore, a relative scale—the atomic mass scale—is used. This scale is sometimes called the atomic weight scale. On this scale, an average of the masses of all the atoms of the naturally occurring mixture of isotopes of a given element is measured relative to the mass of an atom of a standard. 

Compute the mass (in grams) of a single iodine atom if the relative atomic mass of iodine is 126.90447 on the accepted scale of atomic masses (based on 12 as the relative atomic mass of C). 

The isotope of carbon with mass number 12 has been chosen as the defining element for the scale of atomic masses. We define the atomic mass unit, symbol u, as exactly 1/12 of the mass of one atom of carbon-12. Then u = 1.6605655 x 10 kg. The relative atomic mass ofanatom, Ar,is defined by A = m/u, where mis the mass of the atom for example, AXiH) = 1.007825 AJ[ C) = 12 (exactly) = 15.99491. In any macroscopic... 

The early pioneers of chemistry, trying to verify Dalton s atomic theory, could not measure the mass of individual atoms. The best they could do was to measure the masses of equal numbers of atoms (or other known ratios of atoms) of two (or more) elements at a time, to determine their relative masses. They established one element as a standard, gave it an arbitrary value of atomic mass, and used that value to establish the atomic mass scale. The last naturally occurring mixture of isotopes that was used as a standard was oxygen, defined as having an atomic mass of exactly 16 atomic mass units (amu). That standard has been replaced see the next subsection. The atomic mass unit is tiny it takes... 

The scale of atomic weights has as its denominator the integral number 12 as the relative mass of the atom of the principal isotope of carbon,... 

The masses for the elements listed in the table inside the back cover of this text are relative masses in terms of atomic mass units (amu) or daltons. The atomic mass unit is based on a relative scale in which the reference is the C carbon isotope, which is assigned a mass of exactly 12 amu. Thus, the amu is by definition 1/12 of the mass of one neutral c atom. The molar mass of is then... 

Atomic mass units provide a relative scale for the masses of the elements. But since atoms have such small masses, no usable scale can be devised to weigh them in calibrated units of atomic mass units. In any real situation, we deal with macroscopic samples containing enormous numbers of atoms. Therefore it is convenient to have a special unit to describe a very large number of atoms. The idea of a unit to denote a particular number of objects is not new. For example, the pair (2 items), the dozen (12 items), and the gross (144 items) are all familiar units. Chemists measure atoms and molecules in moles. 

A table of atomic masses is given on the inside front cover of this book. Hydrogen atoms, with a mass of about 1/12 that of a carbon atom, have an average atomic mass of 1.00797 amu on this relative scale. Magnesium atoms, which are about twice as heavy as carbon, have an average mass of 24.305 amu. The average atomic mass of oxygen is 15.9994 amu. 

Classical or Newtonian physics describes nature on the macroscopic scales of time, mass, and energy—measured in seconds, kilograms, and joules—to which we are most accustomed. Quantum mechanics and relativity describe deviations from classical mechanics, but they operate more subtly in our experience because their effects are strongest at energy scales much smaller (quantum) or much larger (relativity) than we normally perceive with our own senses. Our interest in this volume is at the microscopic scale, which we will take to mean the scale of individual atoms and molecules distances of a few nanometers or less, masses less than 1000 atomic mass units, and energies of no more than about 10 J. Nevertheless, Isaac Newton s laws of motion for macroscopic bodies are often indispensable in visualizing the motions of microscopic entities, such as individual electrons, atoms, and molecules, sometimes with no adjustment at all. Therefore, it may be useful to review a few topics from classical physics that will show up in the text. 

Relative isotopic, atomic and molecular masses are measured on a scale in which the mass of an atom of carbon-12 is exactly 12 atomic mass units (a.m.u.). 

Figure 3. Relative mass differences for elements that have two or more isotopes, cast as Am/m, where Am is the unit mass difference (Am = 1), and m is the average mass of the isotopes of that element, as a function of atomic number (Z). Note that Am/m is reported in percent, and is plotted on a log scale. Elements that are discussed in this volume shown in large black squares. Other elements that have been the major focus of isotopic studies shown in gray diamonds, and include H, C, O, and S. The relatively large mass differences for the light elements generally produce the largest isotopic fractionations, whereas the magnitude of isotopic fractionation is expected to markedly decrease with increasing mass.

The effects connected with the electron vacuum polarization contributions in muonic atoms were first quantitatively discussed in [4]. In electronic hydrogen polarization loops of other leptons and hadrons considered in Subsect. 3.2.5 played a relatively minor role, because they were additionally suppressed by the typical factors (mg/m). In the case of muonic hydrogen we have to deal with the polarization loops of the light electron, which are not suppressed at all. Moreover, characteristic exchange momenta mZa in muonic atoms are not small in comparison with the electron mass rUg, which determines the momentum scale of the polarization insertions m Za)jme 1.5). We see that even in the simplest case the polarization loops cannot be expanded in the exchange momenta, and the radiative corrections in muonic atoms induced by the electron loops should be calculated exactly in the parameter m Za)/me-... 

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