Bohr shell

The Rydberg constant for deuterium (2H or 2D) is 109,707 cm-1. Calculate (a) the shortest wavelength in the absorption spectrum of deuterium, (b) the ionization energy of deuterium, and (c) the radii of the first three Bohr shells (orbits). 

In essence, Schrodinger concluded that the volume of space in which each pair of electrons could most likely be found defines an orbital and that each orbital can accommodate a maximum of two electrons. Furthermore, he concluded that Bohr s planetary shells can contain more than one such orbital and the orbitals within a given shell may be of different types. Quantum theory shows that the two electrons residing in the first Bohr shell, occupy a single, spherical orbital called a Is orbital (Figure 3.8). 

Table 1. Assignment of electrons to shells according to Bohr s scheme.

Figure 5. Niels Bohr came up with the idea that the energy of orbiting electrons would be in discrete amounts, or quanta. This enabled him to successfully describe the hydrogen atom, with its single electron, In developing the remainder of his first table of electron configurations, however, Bohr clearly relied on chemical properties, rather than quantum theory, to assign electrons to shells. In this segment of his configuration table, one can see that Bohr adjusted the number of electrons in nitrogen s inner shell in order to make the outer shell, or the reactive shell, reflect the element s known trivalency.

Bohr s quantum numbers (n, l, m) have fully entered chemistry, and every chemistry student learns about the symbols Is, 2s, 2p, 3s, 3p, 3d etc. It is hence a startling fact that the simple energy rule has not entered any major chemistry textbooks, as far as I know, and it is still this rule which gives the first explanation of the occurrence of the transition metals, the rare-earth metals, and the over-all structure of the electronic shells of atoms, (p.334). 

The problem is this the third row of the periodic table contains 8, not 18, electrons. It turns out that while quantum numbers provide a satisfying deductive explanation of tbe total number of electrons that any shell can hold, the correspondence of tliese values with the number of elements that occur in any particular period is something of a coincidence. The familiar sequence In which the s, p, d, and f orbitals are filled (see diagram, left) has essentially been determined by empirical means. Indeed. Bohr s failure to derive the order for the filling of the orbitals has been described by some as one of the outstanding problems of quantum mechanics. 

SCF-CI calculations were performed at 20 different intemuclear separations, from 1.2 bohr to 4-00. The lowest separate atom states are, B( P,2p) and H( S) therefore, in order to have a homolytic dissociation and three degenerate 2p orbitals on B we have adopted the closed shell Fock hamiltonian with fractional occupation [23] one electron was placed in the 3(t orbital, correlating with H(ls) at infinite separation, and 1/3 each in the 4it and Itr orbitals correlating with B(2p). 

Bohr s model of a sodium atom. The lone electron in the outer shell is more energetic and less tightly bound to the nucleus than the other electrons. 

Niels Bohr proposed that electrons were particles that circled a nucleus in shells that determined their energies. Helium, he knew, has two electrons. It is a very stable atom, one that refuses to gain... 

Electrons in atoms heavier than helium, Bohr hypothesized, must go into higher energy shells. Thus, lithium, with an atomic number of 3, has two electrons in the n = 1 energy shell, and the third electron must go into a new energy shell with n = 2. 

Quantum numbers can be considered to be approximately equivalent to physical features in the atom proposed by Bohr. The principal quantum number corresponds to one of Bohr s circular energy shells. It is related to the average distance of the electrons from the nucleus. Electrons with larger n values are more energetic and farther from the nucleus. 

Sir Ernest Rutherford (1871-1937 Nobel Prize for chemistry 1908, which as a physicist he puzzled over) was a brilliant experimentalist endowed with an equal genius of being able to interpret the results. He recognized three types of radiation (alpha, beta, and gamma). He used scattering experiments with alpha radiation, which consists of helium nuclei, to prove that the atom is almost empty. The diameter of the atomic nucleus is about 10 000 times smaller than the atom itself. Furthermore, he proved that atoms are not indivisible and that in addition to protons, there must also be neutrons present in their nucleus. With Niels Bohr he developed the core-shell model of the atom. 

The beautiful Bohr atomic model is, unfortunately, too simple. The electrons do not follow predetermined orbits. Only population probabilities can be given, which are categorized as shells and orbitals. The orbitals can only accommodate two electrons. Shells and orbitals can also merge ("hybridization"). In the case of carbon, the 2s orbital and the three 2p orbitals adopt a configuration in the shape of a tetrahedron. Each of these sp3 orbitals is occupied by one electron. This gives rise to the sterically directed four-bonding ability of carbon. 

The shells play a leading role in the structure of the Periodic Table. This graphic representation is borrowed from the Bohr atomic model. Historically, the shells were assigned letters, nowadays... 

M Astatine is isolated in tiny amounts from reactor materials. The Bohr atomic model shows the tightly packed electron shell. One can formally see" the instability. It was the last of the 92 naturally occurring elements to be found. 

Deutsch and Mark compared the classical expression with a theory developed by Bethe.37 Bethe s calculations showed that the ionization cross section for an atomic electron is approximately proportional to the mean square radius of the appropriate n,l electronic shell. Experiment had also shown a correlation between the maximum in the atomic cross section and the sum of the mean square radii of all outer electrons. This led to the replacement of the Bohr radius with the radius of the corresponding subshell the ionization cross section is now given by,... 

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