The correct expression that represents the distribution of electrons in the conduction band is option 'A' which is n(E) = gc(E) * fF(E).

Explanation:
- The distribution of electrons in the conduction band can be determined by considering the density of quantum states (gc(E)) and the Fermi-Dirac probability (fF(E)).

Density of Quantum States (gc(E)):
- The density of quantum states, gc(E), represents the number of available energy states per unit energy range.
- It describes the number of energy states available for electrons to occupy at a given energy level E in the conduction band.

Fermi-Dirac Probability (fF(E)):
- The Fermi-Dirac probability, fF(E), describes the probability of an energy state being occupied by an electron at a given energy level E.
- It takes into account the principle of Pauli exclusion, which states that each energy state can be occupied by a maximum of one electron.
- The Fermi-Dirac probability ranges from 0 to 1, where 0 represents an unoccupied state and 1 represents a fully occupied state.

Combining Density of Quantum States and Fermi-Dirac Probability:
- The expression n(E) = gc(E) * fF(E) represents the number of electrons occupying a particular energy state in the conduction band.
- Multiplying the density of quantum states, gc(E), by the Fermi-Dirac probability, fF(E), gives the number of occupied energy states at a given energy level E.

Explanation of Incorrect Options:
- Option 'B' (n(E) = gc(-E) * fF(E)) does not correctly represent the distribution of electrons in the conduction band because it uses a negative sign for the density of quantum states, which is not physically meaningful.
- Option 'C' (n(E) = gc(E) * fF(-E)) does not correctly represent the distribution of electrons in the conduction band because it uses a negative sign for the Fermi-Dirac probability, which also does not have physical significance.
- Option 'D' (n(E) = gc(-E) * fF(-E)) combines the incorrect aspects of both options 'B' and 'C', and therefore does not represent the correct distribution of electrons in the conduction band.

Conclusion:
- The correct expression to represent the distribution of electrons in the conduction band is option 'A' (n(E) = gc(E) * fF(E)), which correctly combines the density of quantum states and the Fermi-Dirac probability to determine the number of occupied energy states at a given energy level E.