Please do all parts. (1 point each) Give a numerical answer for each of the foll
ID: 2266937 • Letter: P
Question
Please do all parts.
(1 point each) Give a numerical answer for each of the following questions; (a) What is the probability of an electron state at energy E - Ef + 3kT being (b) What is the probability of an electron state at energy E - Ef - SE being (c) What is the probability of an electron state at energy E = EF +6B being (d) The probability that an electron state at E - Eo kT is filled is the same as the (e) The probability that an electron state at E-E0 kT is filled is twice the occupied if T > 0IK occupied if T 0K ccupied if T 0K robability that an electron state at E-Eo - kT is empty. Find Ef probability that an electron state at E = Eo-kT is empty. Find EF. (f) The probability that an electron state at E EakT is filled is the same as the probability that an electron state at E- Eo - bkT is empty. Find Ef. (g) The probability that an electron state at E = E, is empty is 0.5. Find the probability that an electron state at E-E1 + 10kT is occupied.Explanation / Answer
Answer:- From Fermi-Diarac statistics, probability is given by-
f(E) = 1/(1+e(E-EF)/kT).
a) For E= EF + 3kT, f(E) = 1/(1+e3) = 0.047
b) At T=0 K, f(E) = 0.
c) Same as previous, i.e zero.
d) Probability of electron being empty is 1-f(E) =1/1+e(EF - E)/kT. So as per given data we can write-
1/(1+e(E0+kT-EF)/kT) = 1/(1+e(EF - E0 + kT)/kT)
EF = E0 is the answer.
f) In the same way as in part d. We get EF = E0 + ((a-b)/2)kT