Question

Consider the statements in a semiconductor:
(A) There are no free electrons at \(0\;K\).
(B) There are no free electrons at any temperature.
(C) The number of free electrons increases with temperature.
(D) The number of free electrons is less than that in a conductor.

• A. B, C, D are true but A is false
• B. A, B, C are true but D is false
• C. A, C, D are true but B is false
• D. A, B, C and D are all true

Hint:

In semiconductors, conductivity increases with temperature because the number of free electrons and holes increases due to thermal excitation.

Answer 1

The Correct Option is C

Step 1: Examine Statement (A).
At absolute zero, $0\ \text{K}$, every valence electron in a semiconductor stays locked in its covalent bond, so there are no free electrons. Statement (A) is true.
Step 2: Examine Statement (B).
The claim that there are no free electrons at any temperature is wrong, because above $0\ \text{K}$ thermal energy frees some electrons. Statement (B) is false.
Step 3: Examine Statement (C).
As temperature rises, more covalent bonds break and more electron-hole pairs appear, so the number of free electrons increases with temperature. Statement (C) is true.
Step 4: Examine Statement (D).
A semiconductor has far fewer free carriers than a metallic conductor, so its free-electron count is less than that in a conductor. Statement (D) is true.
Step 5: Collect the verdicts.
The true statements are (A), (C) and (D), while (B) is false.
Step 6: Choose the matching option.
Hence the correct choice is \[ \boxed{\text{A, C, D are true but B is false}} \]