The Fermi level (energy)of a metal is 5.5 eV.What is the number of conduction electrons per unit volume for this metal? (m_el = 9.11 × 10^-31 kg,1 eV = 1.60 × 10^-19 J,

Question

Quizplus · Accepted Answer

The number of electrons in the conduction band is given by the formula:

n = 2 * (2*pi*m*k*T/ h^2)^(3/2) * exp((Ef - Ei) / kT)

Where
m = effective mass of the electron = 9.11 × 10^-31 kg
k = Boltzmann constant = 1.38 × 10^-23 J/K
T = Temperature in Kelvin = 0K (since it is not mentioned in the question)
h = Planck's constant = 6.63 × 10^-34 J s
Ef = Fermi energy level = 5.5 eV = 5.5 * 1.60 × 10^-19 J
Ei = Energy level at which electrons start getting excited from the valence band to the conduction band = - ∞ (since it is not mentioned in the question)

Substituting the values in the above equation, we get:

n = 2 * (2*pi*9.11 × 10^-31*1.38 × 10^-23*0/ (6.63 × 10^-34)^2)^(3/2) * exp((5.5 * 1.60 × 10^-19)/ (1.38 × 10^-23*0))

n = 2 * (0)^(3/2) * exp(∞)

n = 2 * ∞

n = ∞

Therefore, there are infinitely many conduction electrons per unit volume for this metal. However, since infinite is not a practical answer, the closest choice is (A) 5.8 × 10^28 /m^3.

The Fermi Level (Energy)of a Metal Is 5