1 (a) The width of an infinite potential well for a free electron of an 1-D material is 10.5 A°. Determine the first four allowed energy levels in eV for this free electron. Also find E2-E1, E3-E2 and E4-E3 in eV. Comment on the separation between successive levels. n?n²h? En %3D 2ma? (b) Suppose for Fermi-Dirac probability distribution function, E-EF = 0.15 eV. Find the temperature at which (i) the fr(E) = 0.05 and (ii) the fr(E) 0.095. Why at higher temperature, the probability of occupancy of a state E > EF is higher? 1 fr (E) = %3D E-EF 1+e kT
1 (a) The width of an infinite potential well for a free electron of an 1-D material is 10.5 A°. Determine the first four allowed energy levels in eV for this free electron. Also find E2-E1, E3-E2 and E4-E3 in eV. Comment on the separation between successive levels. n?n²h? En %3D 2ma? (b) Suppose for Fermi-Dirac probability distribution function, E-EF = 0.15 eV. Find the temperature at which (i) the fr(E) = 0.05 and (ii) the fr(E) 0.095. Why at higher temperature, the probability of occupancy of a state E > EF is higher? 1 fr (E) = %3D E-EF 1+e kT
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Transcribed Image Text:1 (a) The width of an infinite potential well for a free electron of an 1-D material is 10.5 A°.
Determine the first four allowed energy levels in eV for this free electron. Also find E2-E1, E3-E2
and E4-E3 in eV. Comment on the separation between successive levels.
n²n²h?
En
%3D
2mа?
(b) Suppose for Fermi-Dirac probability distribution function, E-EF = 0.15 eV. Find the
temperature at which (i) the ff(E) = 0.05 and (ii) the ff(E) = 0.095. Why at higher temperature,
the probability of occupancy of a state E > EF is higher?
%3D
1
fr (E) =
E-EF
1+e kT
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