Ao, Bohr radius

Ne - number of electrons in molecular unit ao - Bohr-radius... 

Table 9.2. Properties of Rydberg atoms [9-1] R Rydberg constant, ao Bohr radius, n principal quantum number)...

To understand the origins of dispersion forces, let us consider two Bohr atoms, each of which consists of an electron orbiting around a nucleus comprised of a proton, having a radius ao, often referred to as the first Bohr radius . It is obvious that a Bohr atom has no permanent dipole moment. However, the Bohr atom can be considered to have an instantaneous dipole moment given by... 

The symbol ao is the first Bohr radius, approximately 52.9 pm, and to is the permittivity of free space.) As we will see in later chapters, Gaussian orbitals are... 

The probability of finding the electron in the ground state of the hydrogen atom between radii r and r + dr is given by D(r)Ar, where D(r) is the radial probability density function shown in Figure 4.5. The most probable distance of the electron from the nucleus is found by locating the maximum in D(r) (see Problem 4.12 below). It should come as no surprise to discover that this maximum occurs at the value r = ao, the Bohr radius. 

Here y = y/l — a2Z2, T(/ ) is the gamma-function, ao stands for the Bohr radius, and y>s(0) denotes the value of the non-relativistic wave function of an atom at the origin of the coordinates. Multiplier B(y) describes the distribution of the proton charge in the nucleus. For a homogeneous distribution of charge on the surface and in all volume of the spherically-symmetric nucleus, this multiplier B(y) is, respectively,... 

It is instructive to look at the form of the Is, 2s and 3s orbitals (Table 9.1), By Convention, we use the dimensionless variable p = Zr/ao rather than r. Here Z is the nuclear charge number and o the first Bohr radius (approximately 52.9 pm). The quantity Z/n is usually called the orbital exponent, written f. These exponents have an increasing number of radial nodes, and they are orthonormal. 

Show by substitution in the formula given in the text ( Interaction of Light with Matter ) that ao, the radius of the first Bohr orbit for hydrogen, is 5.29 x 10-11 m. 

The unit of length is ao, the first Bohr radius of atomic hydrogen. The Hartree unit of energy is e2/ao, approximately 27.212 electron volts. 

The explicit forms of the radial functions of hydrogenic orbitals Is through 4f are listed in Table 2.1.3, where Z is the nuclear charge of the atom and ao is the Bohr radius ... 

As the nuclei become heavier, the strong attraction of the electrons by the very large nuclear charge causes the electrons to move very rapidly and behave relativistically, i.e. their relative mass (m) increases according to equation 1, and the effective Bohr radius (ao) for inner electrons with large average speeds decreases according to equation 230. 

Table 4. Lamb shift contribution for the ground state of 238U91+ ion (in eV). Here Ro denotes the nuclear radius, M is nuclear mass and ao is the Bohr radius. The finite nuclear-size correction is calculated for a Fermi distribution with (r2)1 /2 = 5.860 0.002 fm. The corrections VPVP (f) and S(VP)E are known only in Uehling approximation. The inaccuracies assigned to these rather small corrections are estimated as the average of the inaccuracies of the Uehling approximation deduced from exact results for the corrections VPVP (e) and SEVP (g),(h),(i)...

At is in units of e2/2 = Ryd.ao with ao being the Bohr radius. The results with the quasi-cubic approximation (QCA) are also listed in parentheses. 

The radial distribution function 47ir2i/ ioo2=(4r2/flo3)exp(—2r/ao), which, when multiplied by dr, is a probability that the electron is in a spherical shell between r and r + dr. This last function peaks at the Bohr radius a0. 

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