To find the number of electrons per unit volume with energy between E and E + dE in a metal we must multiply the number of allowed states per unit volume with energy E by
A) the probability that a state is unoccupied, .
B) the probability that a state is occupied, .
C) the probability that a state is unoccupied, .
D) the probability that a state is occupied, .
E) dE alone.

Question

To find the number of electrons per unit volume with energy between E and E + dE in a metal we must multiply the number of allowed states per unit volume with energy E by
A) the probability that a state is unoccupied, . 
B) the probability that a state is occupied, . 
C) the probability that a state is unoccupied, . 
D) the probability that a state is occupied, . 
E) dE alone.

Quizplus · Accepted Answer

The probability that a state is occupied is given by the Fermi-Dirac distribution function, which gives the probability that a state with energy E is occupied at temperature T. Therefore, to find the number of electrons per unit volume with energy between E and E + dE, we must multiply the number of allowed states per unit volume with energy E by the probability that a state is occupied, which is given by the Fermi-Dirac distribution function.

To Find the Number of Electrons Per Unit Volume with Energy