Question

Assertion (A) : The conductivity of an n-type semiconductor is higher than that of a p-type semiconductor at a given temperature. Reason (R) : The electrons being in the conduction band in n-type semiconductor are more mobile than the holes in the valence band in p-type semiconductor.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

Electrons are more mobile than holes. Hence, n-type semiconductors generally have higher conductivity than p-type semiconductors under similar conditions.

Answer 1

The Correct Option is A

Concept: Conductivity of a semiconductor depends on both the concentration and mobility of charge carriers. \[ \sigma = nq\mu \] where \[ n=\text{carrier concentration}, \] \[ q=\text{charge}, \] and \[ \mu=\text{mobility}. \]

Step 1: Examine the Assertion. In n-type semiconductors, the majority charge carriers are electrons. In p-type semiconductors, the majority charge carriers are holes. Electrons generally have greater mobility than holes. Therefore, for comparable doping levels, n-type semiconductors exhibit higher conductivity. Hence, the Assertion is true.

Step 2: Examine the Reason. Electrons move in the conduction band and possess higher mobility than holes moving in the valence band. Therefore, the Reason is also true.

Step 3: Check the explanation. The higher mobility of electrons directly leads to greater conductivity in n-type semiconductors. Thus, the Reason correctly explains the Assertion. \[ \boxed{\text{(A)}} \]