Mass of one atom

Technological advances in electronics early in the twentieth century led to the invention of the mass spectrometer, a device for determining the mass of an atom (Fig. B.5). Mass spectrometers are described more fully in Major Technique 6 after Chapter 18. Mass spectrometry has been used to determine the masses of the atoms of all the elements. We now know, for example, that the mass of a hydrogen atom is 1.67 X 10 27 kg and that of a carbon atom is 1.99 X 10 26 kg. Even the heaviest atoms have masses of only about 5 X 10-25 kg. Once we know the mass of an individual atom, we can determine the number of those atoms in a given mass of element simply by dividing the mass of the sample by the mass of one atom. 

To tell someone what we mean by l mol, we could give them 12 g of carbon-12 and invite them to count the atoms (Fig. E.l). Because counting atoms directly is impractical, we use an indirect route based on the mass of one atom. The mass of a carbon-12 atom has been found by mass spectrometry to be 1.992 65 X 10 23 g. It follows that the number of atoms in exactly 12 g of carbon-12 is... 

The number of atoms in a unit cell is counted by noting how they are shared between neighboring cells. For example, an atom at the center of a cell belongs entirely to that cell, but one on a face is shared between two cells and counts as one-half an atom. As noted earlier for an fee structure, the eight corner atoms contribute 8 X 1/8 = 1 atom to the cell. The six atoms at the centers of faces contribute 6x1/2 = 3 atoms (Fig. 5.37). The total number of atoms in an fee unit cell is therefore 1 + 3=4, and the mass of the unit cell is four times the mass of one atom. For a bcc unit cell (like that in Fig. 5.34b), we count 1 for the atom at the center and 1/8 for each of the eight atoms at the vertices, giving 1 + (8 X 1/8) = 2 overall. 

SOLUTION (a) We established in Section 5.11 that the length, a, of the side of an fee unit cell composed of spheres of radius r is a = 81/2r. The volume of the unit cell is a3 (Fig. 5.38c). Because there are four atoms in the cell, the mass, m, of one unit cell is four times the mass of one atom (M/NA). The density, d, is therefore... 

Because the masses of nuclides are so small, they are normally reported as a multiple of the atomic mass constant, ma (formerly atomic mass unit, amu). The atomic mass constant is defined as exactly V12 the mass of one atom of carbon-12 ... 

Mass spectrometry allows us to measure masses of individual atoms. Still, there is an enormous difference between the mass of one atom and the masses of samples measured in the laboratory. For example, a good laboratory balance measures mass values from about 10 to 10 g. An atom, on the other hand, has a mass between 10 and... 

The molar mass (MM) of any substance is the mass of one mole of that substance. As described in Section 2-1. each isotope of a particular element has a different mass. Therefore, the mass of one mole of any isotope has a unique value, its isotopic moiar mass. This characteristic molar mass can be found by multiplying the mass of one atom of that isotope by Avogadro s number. For example, mass spectrometry experiments reveal that one atom of carbon-13 has a mass of 2.15928 X 10- g, from which we can calculate the isotopic molar mass of... 

D The average atomic mass of one atom of each element in the molecule... 

Polymers are examples of organic compounds. However, the main difference between polymers and other organic compounds is the size of the polymer molecules. The molecular mass of most organic compounds is only a few hundred atomic mass units (for reference, atomic hydrogen has a mass of one atomic mass unit). The molecular masses of polymeric molecules range from thousands to millions of atomic mass units. Synthetic polymers include plastics and synthetic fibers, such as nylon and polyesters. Naturally occurring polymers include proteins, nucleic acids, polysaccharides, and rubber. The large size of a polymer molecule is attained by the repeated attachment of smaller molecules called monomers. 

Unified Atomic Mass Unit (u) A non-SI unit of mass defined as one twelfth of the mass of one atom of 12C in its ground state and 1.66 x 10-27 kg. The term atomic mass unit (amu) is not recommended to use since it is ambiguous. It has been used to denote atomic masses measured relative to a single atom of 160, or to the isotope-averaged mass of an oxygen atom, or to a single atom of 12C. 

Whenever a very small proton like C—H O—H or N—H is involved in a single bond, the stretching vibrations normally take place at much higher frequency i.e., 3700-2630 cm 1 (or 2.7-3.8 g). It is, however, interesting to note that O—H bond absorbs at 2.8 g (or 3570 cm ), whereas O—D bond absorbs at 3.8 p (or 2630 cm-1). In this specific case, the strengths of the two bonds are more or less the same, but the mass of one atom is almost doubled. 

The unified atomic mass unit (u), previously symbolized as AMU or amu, is defined to be 1/12 of the mass of one atom of isotope 12 of carbon. Therefore,... 

Note Care has to be taken when mass values from dated literature are cited. Prior to 1961 physicists defined the atomic mass unit [amu] based on Vie of the mass of one atom of nuclide 0. The definition of chemists was based on the relative atomic mass of oxygen which is somewhat higher resulting from the nuclides and contained in natural oxygen. 

As we have already seen, the isotopic mass also is the exact mass of an isotope. The isotopic mass is very close but not equal to the nominal mass of that isotope (Table 3.1). Accordingly, the calculated exact mass of a molecule or of a mono-isotopic ion equals its monoisotopic mass (Chap. 3.1.4). The isotope C represents the only exception from non-integer isotopic masses, because the unified atomic mass [u] is defined as of the mass of one atom of nuclide C. 

Relative molecular mass mass of one molecule of a compoimd, with specified isotopic composition, relative to one-twelfth of the mass of one atom of... 

The mass of one atom of any element is infinitessimal and is impossible to measure on any existing balance. A more convenient mass unit was needed for laboratory work, and the concept of the mole emerged, where one mole of an element is a quantity equal to the atomic weight in grams. One mole of carbon, for example, is 12.01 grams, and one mole of iron is 55.85 grams. 

One of the most important nuclear properties that can be measured is the mass. Nuclear or atomic masses are usually given in atomic mass units (amu or u) or their energy equivalent. The mass unit u is defined so that the mass of one atom of 12C is equal to 12.0000. .. u. Note we said atom. For convenience, the masses of atoms rather than nuclei are used in all calculations. When needed, the nuclear mass mllucl can be calculated from the relationship... 

There are at present 118 different elements known. The atoms of these elements differ in mass because of the different numbers of protons, neutrons and electrons they contain. The actual mass of one atom is very small. For example, the mass of a single atom of sulfur is around ... 

To find the mass of one atom compared to another, we assign a mass of 12 atomic mass units to carbon atoms having 6 protons and 6 neutrons in their nuclei. Other isotopes of carbon exist in nature in very small quantities. Carbon-13, with 6 protons and 7 neutrons, is 1.11% of a sample of carbon. Carbon-14, with 6 protons and 8 neutrons, is also present in tiny amounts in a carbon sample. 

In 1808 John Dalton proposed his atomic theory, which included the statement that when atoms of two or more elements combine to form a compound, they combine in a definite ratio by number of atoms and by mass. This is called the law of definite proportions. This provided a means to determine the mass of one atom relative to another. It was necessary to assign a mass to one element to find the mass of another element in a compound. Today we use the most common carbon isotope, assigned a mass of 12.00 atomic mass units (amu), as the basis for comparative weights of the atoms. 

Some numbers are exact. These include k (3.14159. . . ), numbers arising from counting (e.g., the number of experimental determinations of an observed measurement), and numbers which involve a definition (the mass of one atom of 12C is exactly 12 u and the conversion of cm to m involves exactly 10 2 m/cm). 

Other numerical values are exact by definition. For example, the atomic mass scale was established by fixing the mass of one atom of 12C as 12.000 Ou. As many more zeros could be added as desired. Other examples include the definition of the inch (1 in = 2.5400 cm) and the calorie (1 cal = 4.184 00 J). 

Consider, for example, carbon monoxide. The mass of one mole of carbon-12 atoms is exactly 12 g dividing by Avogadro s number (and converting to kg) gives the mass of a single carbon-12 atom as 1.9926 x 10 26 kg. The mass of one mole of oxygen-16 atoms is 15.9949 g, so the mass of one atom is 2.6560 x 10-26 kg (masses in amu for many different isotopes are listed in Appendix A). The reduced mass y = memo/ me + mo) is then 1.1385 x 10-26 kg. 

Molar masses of chemical compounds are equal to the sums of the molar masses of all the atoms in one molecule of that compound. If we have a chemical compound like NaCI, the molar mass will be equal to the molar mass of one atom of sodium plus the molar mass of one atom of chlorine. If we write this as a calculation, it looks like this ... 

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