Which of the following statements is TRUE? (a) The energy of free electron is pr

Question

Which of the following statements is TRUE? (a) The energy of free electron is proportional to k, where k is the electron wave vector and constant of proportionality is h. (b) The energy of a free electron is proportional to k^2, where k is the electron wave vector and constant of proportionality is h^2 (c) The energy of a free electron is proportional to k^2, where k is the electron wave vector and constant of proportionality is h^2/2m. (b) The energy of a free electron is proportional to k^2, where k is the electron wave vector and constant of proportionality is h^2/2m. (e) The number of electrons in the conduction band (in #/cm^3) can be determined by integrating, e product of the density of states function and the probability of occupancy, over the energy range of the band. (f) The mass of an electron in a semiconductor depends upon the first derivative of the E-k diagram but is independent of the direction in which it is traveling. (g) GaAs is an example of a direct bandgap semiconductor whereas GaP is an indirect bandgap semiconductor. (h) Fermi Dirac Statistics give the probability of occupancy of a state by electrons at high temperatures whereas the Maxwell Boltzmann Statistics give the probability of occupancy of a state by electrons at low temperature. [A] (a), (c), (h) [B] (b), (d), (e) [C] (b), (f), (h) [D] (c), (e), (8) [E] (b), (c), (g)

Explanation / Answer

Solution:

The energy is given by

E = Ex +  Ey +  Ez

E = (h2 / 2m ) ( Kx2 + Ky2 + Kz2 )

E = (h2 / 2m ) K2  

where , K is a wave vector

so option b is true not option c because mass of an electron changes which is not a constant

even d is not an option because energy is directly proportional to K2

so the option [C] is the answer.

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