D

correct expression is...1/{1+(exp[(E-Ef)/kT]}

The Fermi-Dirac distribution function provides the probability of occupancy of energy levels by electrons.

Fermi-Dirac Distribution Function:
The Fermi-Dirac distribution function is a mathematical expression that describes the probability of an energy state being occupied by a fermion (a particle with half-integer spin, such as electrons) at a given temperature. It is named after Enrico Fermi and Paul Dirac, who independently developed the concept.

The Fermi-Dirac distribution function, denoted as fF(E), is given by:

fF(E) = 1 / [exp((E - EF) / (kT)) + 1]

Where:
- fF(E) is the Fermi-Dirac distribution function as a function of energy (E).
- E is the energy of the state.
- EF is the Fermi energy, which represents the maximum energy level that can be occupied by a fermion at absolute zero temperature.
- k is the Boltzmann constant.
- T is the temperature in Kelvin.

Explanation:
Among the given options, the expression that represents the Fermi probability function is option 'B':

fF(E) = exp(-[EF - E] / (kT))

This expression is equivalent to the Fermi-Dirac distribution function. Let's break down the expression and understand its components:

- The exponential function exp(x) is the inverse of the natural logarithm and is commonly used in mathematical calculations.
- The term (EF - E) represents the difference between the Fermi energy and the energy of the state E. This difference determines the probability of occupation.
- The division by (kT) scales the difference in energy with respect to temperature, where k is the Boltzmann constant and T is the temperature in Kelvin.
- The negative sign in the exponent accounts for the fact that as the energy of the state increases, the probability of occupation decreases.

The main difference between option 'B' and the correct expression is the sign in the exponent. In option 'B', the sign is negative, while in the correct expression, the sign is positive. The correct expression aligns with the definition of the Fermi-Dirac distribution function, where the exponent is positive and determines the probability of occupation.

Therefore, the correct expression representing the Fermi probability function is:

fF(E) = exp(-[E - EF] / (kT))