O modelo atômico de Bohr e as abordagens para seu ensino na escola média

The teaching of modern and contemporary Physics subjects in high school is indispensable and it was already justified by several researchers. Among the subjects which must be taught, there is, for instance, Bohr atomics model. However, as it was noticed in literature review, many didactic materials do not deal with this model adequately, since that they do not take into account Bohr ideas, which involved Planck studies on black-body radiation, Einsten theory for photoelectric effect, Rutherford experiences and atomics model and the empiric results upon the spectrums of chemical elements emission. From that, it is extremely important teaching through approaches which potentialize the learning of the model proposed by Niels Bohr. On the other hand, teachers from high schools cannot have clearness about which approaches can be applied for teaching the mentioned model. Thus, it is presented some possibilities for teaching Bohr atomics model, with examples and justifications for the use of each one. Special treatment was attributed to the teaching from Science History and Philosophy, from the reading of scientific diffusion and original scientific texts, from analogies, from comic strips and from computer simulations.

Cross sections for transfer ionization in ion-helium collisions

A simple model has been developed within the independent-particle model (IPM) based on the Bohr-Lindhard model and classical statistical model. Cross sections for transfer ionization of helium by ions A(q+) (q = 1-3) are calculated for impact energies between 10 and 6000 keV/u. The calculated cross sections are in good agreement with the experimental data of helium by He(1-2)+ and Li(1-3)+.

Transfer ionization of helium in collisions with Cq+ and Oq+ (q=1-3)

Cross-section ratios sigma(TI)/sigma(SC) of transfer ionization (TI) to single capture (SC) of Cq+- and Oq+-He (q = 1 - 3) collisions in the energy range of 15-440 keV/u (0.8-4.2 v(Bohr)) are experimentally determined. It is shown that sigma(TI)/sigma(SC) strongly depends on the projectile velocity, and there is a maximum for E(keV/u)/q(1/2) approximate to 150. Combining the Bohr-Lindhard model and the statistical model, a theoretical estimate is presented, in reasonable agreement with the experimental data when E(keV/u)/q(1/2) > 35.

L-shell ionization accompanied by one-electron capture in Cq+, Oq+ (q=2,3)-Ne collisions

The L-shell ionization processes of a Ne gas target associated with single-electron capture by bombardment of Cq+ and Oq+ (q=2,3) are investigated using the projectile-recoil-ion coincidence method in the energy range from 80 to 400 keV/u (v(p)=1.8-4 a.u.). The cross-section ratios (R-k1) of k-fold ionization to single capture are compared with the results for He2+-Ne collisions by Dubois [Phys. Rev. A 36, 2585 (1987)]. All the velocity dependences are quite similar. The ratios increase as the projectile energy increases in the lower-energy region, reach the maxima for projectile energies around E-max=160q(1/2) keV/u, and then decrease at higher energies. These results qualitatively agree with our calculations in terms of the Bohr-Lindhard model within the independent-electron approximation.

The Hydrogen Atom: The Bohr Model in Detail

The Bohr Model for the Hydrogen Atom's electron is discussed in detail, with a recapitulation of angular momentum and a detailed discussion of relevant units (out of the cgs system).

The statistical bootstrap model

A review is presented of the statistical bootstrap model of Hagedorn and Frautschi. This model is an attempt to apply the methods of statistical mechanics in high-energy physics, while treating all hadron states (stable or unstable) on an equal footing. A statistical calculation of the resonance spectrum on this basis leads to an exponentially rising level density ρ(m) ~ cm^-3 e^βom at high masses.

In the present work, explicit formulae are given for the asymptotic dependence of the level density on quantum numbers, in various cases. Hamer and Frautschi's model for a realistic hadron spectrum is described.

A statistical model for hadron reactions is then put forward, analogous to the Bohr compound nucleus model in nuclear physics, which makes use of this level density. Some general features of resonance decay are predicted. The model is applied to the process of NN annihilation at rest with overall success, and explains the high final state pion multiplicity, together with the low individual branching ratios into two-body final states, which are characteristic of the process. For more general reactions, the model needs modification to take account of correlation effects. Nevertheless it is capable of explaining the phenomenon of limited transverse momenta, and the exponential decrease in the production frequency of heavy particles with their mass, as shown by Hagedorn. Frautschi's results on "Ericson fluctuations" in hadron physics are outlined briefly. The value of β_o required in all these applications is consistently around [120 MeV]^-1 corresponding to a "resonance volume" whose radius is very close to ƛ_π. The construction of a "multiperipheral cluster model" for high-energy collisions is advocated.

The Kepler Problem (the road to Bohr)

The classical Kepler problem is reviewed in depth in preparation to studying the Bohr model of the atom.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.