Hydrogen atom rest mass

The units we use in daily life, such as kilogram (or pound) and meter (or inch) are tailored to the human scale. In the world of quantum mechanics, however, these units would lead to inconvenient numbers. For example, the mass of the electron is 9.1095 X J0 31 kg and the radius of the first circular orbit of the hydrogen atom in Bohr s theory, the Bohr radius, is 5.2918 X 10 11 m. Atomic units, usually abbreviated as au, are introduced to eliminate the need to work with these awkward numbers, which result from the arbitrary units of our macroscopic world. The atomic unit of length is equal to the length of the Bohr radius, that is, 5.2918 X 10 n m, and is called the bohr. Thus 1 bohr = 5.2918 X 10"11 m. The atomic unit of mass is the rest mass of the electron, and the atomic unit of charge is the charge of an electron. Atomic units for these and some other quantities and their values in SI units are summarized in the accompanying table. 

We know a great deal about the nature of the universe. For instance, the element hydrogen makes up about 75% of all the mass in the universe. In terms of number, about 90% of all atoms in the universe are hydrogen atoms, and most of the rest of the atoms in the universe are helium. All the other heavier elements make up just one to two percent of the total. Interestingly, the most abundant element on Earth (in number of atoms) is oxygen (O ). Oxygen accounts for about 50% of all the elements found in the Earth s crust, and silicon, the second most abundant element, makes up about 25%. Silicon dioxide (SiO ) accounts for about 87% of the total Earth s mass. Sfiicon dioxide is the main chemical compound found in sand and rocks. 

An atomic unit of length used in quantum mechanical calculations of electronic wavefunctions. It is symbolized by o and is equivalent to the Bohr radius, the radius of the smallest orbit of the least energetic electron in a Bohr hydrogen atom. The bohr is equal to where a is the fine-structure constant, n is the ratio of the circumference of a circle to its diameter, and is the Rydberg constant. The parameter a includes h, as well as the electron s rest mass and elementary charge, and the permittivity of a vacuum. One bohr equals 5.29177249 x 10 meter (or, about 0.529 angstroms). 

The atomic unit of length is the radius of the first Bohr orbit in the hydrogen atom when the reduced mass of the electron is replaoed by the rest mass tne. Thus the atomic unit of length is... 

This is just twice the ionization potential of the hydrogen atom if the re duced mass of the electron is replaced by the rest mass. One atomic unit of energy is equivalent to twice the Rydberg constant for infinite mass. 

Finally, Eqs. (108) and (109) may be easily adapted to emission by atomic transitions. For the hydrogen atom, one only needs to substitute reduced masses as appropriate. The same is true, as a first approximation, for more complex atoms, where an electron undergoing a transition sees the rest of the atom as a positive charge. Computer animations of such transitions have been independently produced by Barbosa and Gonzalez [40],... 

Fig. 11. Total cross section for the interaction of relativistic positronium atoms with carbon as a function of the kinetic energy expressed in the rest masses of the incident atom (T = 7—1). The solid curve is the theoretical dependence, - the measured value. The arrow marks the region (7 < 1.2) investigated in experiments on the interaction of hydrogen atoms with carbon...

Because protons and electrons have equal but opposite charges, a neutral atom must contain equal numbers of protons and electrons. But solving this mystery led to another the mass of an atom (except hydrogen atoms) is known to be greater than the combined masses of the atom s protons and electrons. What could account for the rest of the mass Hoping to find an answer, scientists began to search for a third subatomic particle. 

Making allowance for the energy carried away by the 2 neutrinos (2 x 0.25 MeV) this leaves a total of 26.22 MeV for radiation, i.e. 4.20 pJ per atom of helium or 2.53 x 10 kJ mol . This vast release of energy arises mainly from the difference between the rest mass of the helium-4 nucleus and the 4 protons from which it was formed (0.028 atomic mass units). There are several other peripheral reactions between the protons, deuterons and He nuclei, but these need not detain us. It should be noted, however, that only 0.7% of the mass is lost during this transformation, so that the star remains approximately constant in mass. For example, in the sun during each second, some 600 x 10 tonnes (600 x 10 kg) of hydrogen are processed into 595.5 x 10 tonnes of helium, the remaining... 

Mass defect B) - Defined by fi = Zm( H) + Nm - m, where Z is the atomic number, m( H) is the mass of the hydrogen atom, N is the neutron number, m is the rest mass of the neutron, and is the mass of the atom in question. Thus Bc can be equated to the binding energy of the nucleus if the binding energy of atomic electrons is neglected. [1]... 

In this text, we shall emphasize compounds with molecular ions that can be identi-hed or deduced with reasonable certainty. If the molecular ion is present, it must have the highest m/z in the spectrum, excluding the effects of isotopes. Examples are shown for methane (Eig. 10.2, Table 10.2), methanol (Fig. 10.3, Table 10.3), and benzene (Eig. 10.4, Table 10.1). In each case, the molecular ion was very abundant and not difficult to identify. This is not always the case, as will be seen in later examples. The student should note that in most of the mass spectra used as examples, the molecular ion m/z value is marked by a black triangle on the x-axis. The x-axis is in units of m/z while the y-axis is relative abundance, even though these units are not marked on the spectra. The most intense peak is set to 100% and the rest of the peaks normalized to that peak. The structure of the compound is also shown on the spectrum, using a shorthand method that does not show the hydrogen atoms or the carbon atoms. The methanol spectrum (Fig. 10.3) demonstrates clearly that the molecular ion is not the base peak in the spectrum the fragment ion at m/z = 31 is the most abundant ion. 

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