Atomic mass calculation

Atomic masses calculated in this manner, using data obtained with a mass spectrometer can in principle be precise to seven or eight significant figures. The accuracy of tabulated atomic masses is limited mostly by variations in natural abundances. Sulfur is an interesting case in point. It consists largely of two isotopes, fiS and fgS. The abundance of sulfur-34 varies from about 4.18% in sulfur deposits in Texas and Louisiana to 4.34% in volcanic sulfur from Italy. This leads to an uncertainty of 0.006 amu in the atomic mass of sulfur. 

The mass of the electron is 9.110 X 10 g, which is much less than either a proton or neutron. Because the masses of subatomic particles are so small, chemists use a unit called an atomic mass unit (amu). An amu is defined as one-twelfth of the mass of the carbon atom with 6 protons and 6 neutrons, a standard with which the mass of every other atom is compared. In biology, the atomic mass unit is called a Dalton (Da) in honor of John Dalton. On the amu scale, the proton and neutron each have a mass of about 1 amu. Because the electron mass is so small, it is usually ignored in atomic mass calculations. 

To determine atomic mass, calculate the contributitxi of each isotope to the total atomic mass, by multiplying the mass of each of the isotopes by its percent abundance/lOO and adding the results. 

Isotopes and percent abundances of thallium and rubidium are now included in atomic mass calculations. 

Fig. 1-5. Dependence of Qp- values of the Ru, Rh, and Pd isotopes on the nucleon number. The dots represent the data evaluated by Wapstra et al. [22, 24] the dashed lines connect values obtained from empirical systematic trends [24]. The Qp- values derived from the atomic masses calculated by Liran and Zeldes [27] for the decay of the isotopes of Tc (o), Ru (a), Rh ( ), and Pd (v) are also shown. On the right scale the Qg values for the decay in the reverse direction, like Ru, Tc, are given.

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 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. 

Fig. 11. Abundance mass spectra of differently charged hot CgoLL clusters evaporating atoms calculated with a Monte-Carlo simulation (the Li and Cgg isotope distributions are included). Energies required to remove Li atoms were calculated using the MNDO method. The peaks at x = 12 and at x = 6 + n (where n is the cluster charge) observed in experiment (Fig. 9) are well reproduced.

In the infinite sum each successive term is smaller than the previous by a constant factor ( -hujVT which is <1), and can therefore be expressed in a closed form. Only the vibrational frequency is needed for calculating the vibrational partition function for a harmonic oscillator, i.e. only the force constant and the atomic masses are required. 

Only the vibrational frequencies are needed, which can be calculated from the force constant matrix and atomic masses. 

We interpret this to mean that, in elemental chlorine, 75.53% of the atoms have a mass of 34.97 amu, and the remaining atoms, 24.47% of the total, have a mass of36.97 amu. With this information we can readily calculate the atomic mass of chlorine using the general equation... 

If the atomic mass of an element is known and if it has only two stable isotopes, their abundances can be calculated from the general equation cited above. 

Knowing Avogadro s number and the atomic mass of an element, it is possible to calculate the mass of an individual atom (Example 3.2a). You can also determine the number of atoms in a weighed sample of any element (Example 3.2b). 

Clearly, the plot of Figure 8-3 contains information about the distribution of kinetic energies. From the rate of rotation of the discs and the distance between them we can calculate the velocity an atom must have to condense on a particular pie slice. From the atomic mass and its velocity, we learn the atom s kinetic energy. Figure 8-4 shows the result. At a temperature Tt... 

The relative molecular mass for sulphuric acid, H2S04, is calculated from the relative atomic masses as follows ... 

The greater the mass of an individual atom, the greater the molar mass of the substance. However, most elements exist in nature as a mixture of isotopes. We saw in Section B, for instance, that neon exists as three isotopes, each with a different mass. In chemistry, we almost always deal with natural samples of elements, which have the natural abundance of isotopes. So, we need the average molar mass, the molar mass calculated by taking into account the masses of the isotopes and their relative abundances in typical samples ... 

STRATEGY First calculate the average atomic mass of the isotopes by adding together the individual masses, each multiplied by the fraction that represents its abundance. Then obtain the molar mass, the mass per mole of atoms, by multiplying the average atomic mass by Avogadro s constant. 

Identify a process to solve the problem. The question asks about the volume of one silver atom. Mass and volume are related through density p — mj V. From this equation, we can calculate the total volume of the silver atoms. The problem also gives the total number of silver atoms transferred from the wire to the spoon. The volume of a single atom is the total volume divided by the number of atoms. Oftentimes, a flow chart helps to summarize the process ... 

Two forms of the same element are called isotopes. The isotopes of an element have the same atomic number but have different atomic masses. Iron has several isotopes that, when weighted by their naturally occurring abundance, gives an average mass of 55.845 amu. A simple example would be an element with only two isotopes, one with a mass of 10 amu, the other of 12 amu. If the isotopes were equally common, then the average atomic mass for that element would be 11. If 90% of the element occurred naturally as the isotope with a mass of 10 amu, then the average atomic mass would be 10.2, as calculated below ... 

Increasingly, new attempts to use basic chemistry to separate substances from radioactive material were meeting with failure. In many cases, two substances which were known to have different radioactive properties and molecular masses simply could not be separated from one another and appeared chemically identical. By 1910, this problem led Soddy to speculate that there were different forms of the same element (Soddy 1910). By 1913 he was confident of this interpretation and coined the term isotope to describe the various types of each element, recognizing that each isotope had a distinct mass and half-life (Soddy 1913b). In the same year he wrote that radiothorium, ionium, thorium, U-X, and radioactinium are a group of isotopic elements, the calculated atomic masses of which vary from 228-234 (a completely accurate statement- we now call these isotopes Th, °Th, Th, Th respectively). Soddy received the... 

The activation energy for evaporation of over-stechiometric zinc atoms Zn calculated from the tilt of this line is 32 kcal/gram/atom. This means that evaporation heat of superstechiometric zinc atoms (Zn ) from zinc oxide found in these experiments agrees well with the corresponding value found in [31] by mass-spectrometry. 

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