Question

failure of free electron theory with reference to hall effect

Answer 1

Answers

Modified electron theory of the hall effect.—It is generally supposed that the simple electron theory of conduction leads to a negative coefficient for this effect and that the positive coefficients found for many metals are anomalous. But if we suppose the free path instead of the free time of motion of the electrons to be independent of the velocity, then in the case of isotropic conductors, the effect comes out zero. Considering the group of electrons having a given speed immediately after collision with molecules, those moving with the electric field  E  will be retarded and will be more deflected by a magnetic field  H than those moving against  E , giving a positive coefficient, but electrons moving at right angles to both E  and  H  will give a negative coefficient, and assuming all directions equally probable, the resultant effect for each group and therefore for all is found to be zero. By slight modification of the assumptions of the simple theory, either positive or negative coefficients may be obtained. In the case of a crystal, on account of the asymmetry of free paths, a positive effect might be expected for one orientation and a negative for one at right angles. Though the experimental results are not as simple as this, the fact that the Hall effect has never been detected for mercury and that nearly all metals with negative coefficients have face-entered crystal lattices, while those with positive coefficients have body-centered or hexagonal lattices, indicates that the distribution of free paths with reference to  E  and  H  is of importance.