Silicon is doped with arsenic. The weakly bound electron fromarsenic moves in th

Question

Silicon is doped with arsenic. The weakly bound electron fromarsenic moves in the first Bohr orcit around a silicon atom. The first Bohr orbit has a radius given by : ao=(4ohbar2) /(me2) Due to the effects of screening, it is necessary to replace0 with the electric permittivity=k0, where k is the dielectric constant (k =11.7 for silicon). Using this information, find the binding energyof E0 for the first Bohr orbit of the extra electron insilicon in eV. Silicon is doped with arsenic. The weakly bound electron fromarsenic moves in the first Bohr orcit around a silicon atom. The first Bohr orbit has a radius given by : ao=(4ohbar2) /(me2) Due to the effects of screening, it is necessary to replace0 with the electric permittivity=k0, where k is the dielectric constant (k =11.7 for silicon). Using this information, find the binding energyof E0 for the first Bohr orbit of the extra electron insilicon in eV.

Explanation / Answer

Given radius is of the Bohr's radius is : ao= (4ohbar2) /(me2) From this velocity is :             m v ao   = n h / 2           velocity (v) = e2 / 2 n h o Electron energy is :                   Potential energy + kinetic energy            Potentialenergy    = e / 4 oao                                        = - m e4 / 4 n2 h2o2           Kineticenergy       = 1/2 mv2                                       =   m e4 / 8 n2 h2o2 Binding energy of electron for the first Bohrorbit    is :                        E   =   - m e4 / 8 n2h2 o2 ----------(1) m = mass of electron = 9.11 x 10-31 kg ; e = 1.602 x 10-19 C ; n = 1 ; h = 6.624 x 10-34 Plugg the values in equation (1) to get the value ofenergy. Hope this helps u!                  

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