Atomic radius determination

In previous chapters, we saw that the volume of an atom is taken up primarily by its electrons (Chapter 2) occupying quantum-mechanical orbitals (Chapter 7). We also saw that these orbitals do not have a definite boundary but represent only a statistical probability distribution for where the electron is found. So how do we define the size of an atom One way to define atomic radii is to consider the distance between nonbonding atoms that are in direct contact. For example, krypton can be frozen into a solid in which the krypton atoms are touching each other but are not bonded together. The distance between the centers of adjacent krypton atoms—which can be determined from the solid s density—is then twice the radius of a krypton atom. An atomic radius determined in this way is called the nonbonding atomic radius or the van der Waals radius. The van der Waals radius represents the radius of an atom when it is not bonded to another atom. 

Atomic radii. The radii are determined by assuming that atoms in closest contact in an element touch one another. The atomic radius is taken to be one half of the closest internuclear distance, (a) Arrangement of copper atoms in metallic copper, giving an atomic radius of 0.128 nm for copper, (b) Chlorine atoms in a chlorine (Cl2) molecule, giving an atomic radius of 0.099 nm for chlorine. 

This relation offers an experimental way of determining the atomic radius of a metal, if the nature and dimensions of the unit cell are known. 

Calculate the apparent volume (in pnt1) and radius (in pm) of a helium atom as determined from the van der Waals parameters,... 

Iron crystallizes in a bcc structure. The atomic radius of iron is 124 pm. Determine (a) the number of atoms per unit cell (b) the coordination number of the lattice (c) the length of the side of the unit cell. 

Assume there exists some hypothetical metal that exhibits ferromagnetic behavior and that has a simple cubic structure, an atomic radius of 0.153 nm, and a saturation flux density of 0.76 tesla. Determine the number of Bohr magnetons per atom for this material. 

An estimate of die size of the proton and an understanding of the structure of the hydrogen atom resulted from two major developments in atomic physics the Rudierford scattering experiment (1911) and the Bohr model of die atom (1913). Rutherford showed that the nucleus is vanishingly small compared to the size of an atom. The radius of a proton is on the order of 10-13 centimeter as compared with atomic radii of 10-3 centimeter, Thus, the size of a hydrogen atom is determined by the radius of the electron orbits, but the mass is essentially that of the proton,... 

Potassium crystallizes in a bcc structure. The atomic radius of potassium is 235 pm. Determine... 

Determine the density of each of the following metals from the data given (a) nickel (fee structure, atomic radius 125 pm) (b) rubidium (bcc structure, atomic radius 250 pm). 

Use the Interactive Periodic Table in eChapter 5.15 to determine the trend in atomic radius as you move across a period and as you move down a group. Explain the factors that account for these trends. 

The electron cloud around an atom makes the concept of atomic size somewhat imprecise. Even so, it is useful to refer to an atomic size or an atomic radius. Operationally, one can divide the experimentally determined distance between the centers of two chemically bonded atoms to arrive at the two atomic radii. If the bonding is covalent (see Chapter 9), the radius is called a covalent radius if the bonding is ionic, the radius is an ionic radius. The radius for a nonbonded situation may also be defined in terms of the distance of closest nonbonding approach and is called a van der Waals radius. These concepts of size are illustrated in Fig. 8-6. 

We may expect that the radius of the atom, if that expression has a meaning, will be of the order of magnitude of the radius of the largest orbit ordinarily occupied by an electron in the neutral atom. In the case of copper this is the 4s orbit, while in the copper ion it is the 3d. In the next section we tabulate such quantities for the atoms, and in later chapters we shall find these radii of interest in connection with the dimensions of atoms as determined in other ways. 

For the monatomic case ( = = 1), was definedto be a parameter where the latter was taken to be the atomic radius from the Optimized Potentials for Liquid Simulations (OPLS)2°6 force field less 0.09 A, which is an empirical adjustment. In the multicenter case, is defined numerically by a new procedurei that could be thought of as an approximation to the solutions of Equations [6]—[10]. In this procedure, is chosen so that the Gp derived as in a monatomic case is equal to the Gp determined via numerical integration. Thus, one considers M spherical shells i around each atom k and calculates... 

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