Question

1.how to prove average electron energy

2.how to prove Fermi energy level at 0K

Answer 1

Single Portiche energy eigenstates for a system of particles given by to a box are En n² f. 2m L² Fermienergy from a single particle is geven by definition, the value of it energy that exhausts all the possible stakes geven by N indistinguishable particles in the Case of hand for fornians lelections) this is geven by h2K² 2012 ne line h²a2 N² 2m12 = 1/2 because ч can place at most 2 Fernians with different &find in same state. Etoral NJ IN (E+ Ef (Ni)) - Nto + H3N3 24mL Etorul to + Ef 3 Eaug Fermi energy at ok Epo Total Number of electrons (free) is a metal is given by Sucede where Fle) (6) Hence ICE)

& CE) de Efo of M= They g(e) de FS FCE) SFE) JEI DE Bat fe) t al T=ok for € effo And i f€) = o at T=ok for E> Efo. Hence second integral is zero & in fost lastegral we put f(E)=1 N Ef geldt Ato; f@=- results g E) = E) for N = tfab) El de Value of n[E)de = puthing SEAVm32 € 22 de 82 AV ml El de hos Ce co-edit as] h3 - T = ok for fcffo stence Efo 8RKV32 Ele de th . 11 SKV (am Efo 3 h² ha 3N Efo electrony penumis fo 1) vidume) Efo 31 8
P.S : Please do give a thumbs up since we as an expert take pain and take our time out by typing answer in lucid language and putting best of our knowledge at your doorstep.
Thank you