Question

Please be neat with solution..Thanks.

(a) What is the probability of finding an electron in silver with energy 1.016EF > Ef at temperature at 296 K? Do you need the Fermi energy of silver to do this problem? (b) What is the probability of finding an electron in silver with energy 0.984EF < Ef at the temperature of 296 K? (c) ADD the number of part (b) TO THE NUMBER YOU GOT IN PART (a). WHAT IS THE VALUE OF THE SUM? DOES THIS SEEM REASONABLE? IS IT CLOSE TO ONE? EXPLAIN.

Answer 1

As we know that formula of probability of finding an electron in a material can be given as,

P = 1/e^((E-Ef)/KbT) + 1

Where, E is the energy of electron

Ef is the fermi energy

Kb is the Boltzmann constant

T is the temperature

(a).

Yes we need the fermi energy to calculate the problem and taking Ef = 5.5eV

Now according to given problem, by putting the values in above equation,

P1 = 1/e^((1.016Ef-Ef)/KbT) +1

P1 = 1/e^((0.016 × 5.5)/8.62×10^-5 ×296) + 1

P1 = 0.0308009475

(b).

Now putting the value in the given equation,

P2 = 1/e^((-0.016 × 5.5)/8.62×10^-5 × 296) +1

P2 = 0.969199053

(c).

P = P1 + P2

P = 0.0308009475 + 0.969199053

P = 1