the energy levels of electrons of mass m and charge e is confined in an area A i

Question

the energy levels of electrons of mass m and charge e is confined in an area A in xy-plane with uniform magnetic field B applied in the z- direction are given by ,En=(n+1/2)eBh/mc , n= 0,1,2...
the degeneracy of each level is eBA/hc.the lowest level is completly filled and others are empty.the fermi energy h2N/2mA, where N is the total number of electrons, is
1. coincident with the n=0 level
2. coincident with the n=0 level
3. midway between the n=0 and n=1 levels
4. midway between the n=1 and n=2 levels
(please write with better explanation)

Explanation / Answer

The particle electron was conceived as a small material particle of mass m and carrying a negative electrical charge of magnitude e = 4.803207 x 10-10 esu. The electromagnetic force on a particle of charge q and mass m is given by the Lorentz force, f = q[E + (1/c)v x B], where E is the electric field in statvolt/cm, B the magnetic field in gauss, and v the velocity in cm/s. I will use Gaussian (cgs) units here and in what follows, but will give the equivalents in MKS units in most cases. The use of MKS units in atomic physics can be inconvenient, especially when magnetic fields are considered. Otherwise simple equations sprout meaningless conversion factors with o and o and 4's in them, and dimensional analysis is confused. I will avoid this whole mess by using Gaussian units. The conversions 10,000 gauss = 1 T and 300 V = 1 statvolt are useful in expressing results in practical units. The electronic charge in MKS is e = 1.602177 x 10-19 C. (Multiply by c/10, where c is in cm/s, to get esu). The electron-volt (eV) unit of energy is 1.602 x 10-19 J or 1.602 x 10-12 erg. For more information on units.

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