Question

Two statements are given — one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the options below:

(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.

Assertion (A): The electrical conductivity of a pure Ge crystal increases with increase in its temperature.

Reason (R): The number of electrons excited by thermal excitation from the valence band to the conduction band, in a semiconductor, increases with increase in temperature.

• A. A
• B. B
• C. C
• D. D

Hint:

In an intrinsic semiconductor heating creates more electron-hole pairs. This raises conductivity, so both statements are true and R explains A.

Answer 1

The Correct Option is A

Step 1: Understand the statements:
Assertion (A) says that the conductivity of pure Ge rises when the temperature rises. Reason (R) says that more electrons jump from the valence band to the conduction band at higher temperature.
We must check each statement and then see whether R explains A.

Step 2: Check the Reason (R):
In pure Ge the band gap is small (about 0.7 eV). At 0 K the valence band is full and the conduction band is empty.
As the temperature goes up, thermal energy lifts more electrons across the gap. Each such electron leaves behind a hole. So the number of carriers grows quickly with temperature. R is TRUE.

Step 3: Check the Assertion (A):
Conductivity is \(\sigma = e\,(n_e \mu_e + n_h \mu_h)\), where \(n_e, n_h\) are electron and hole densities and \(\mu\) is mobility.
In a semiconductor, \(n_e\) and \(n_h\) rise very fast with temperature. This rise outweighs the small fall in mobility. So \(\sigma\) increases. A is TRUE.

Step 4: Does R explain A?:
Yes. The increase in conductivity is caused by the larger number of thermally excited electrons and holes. So R is the correct explanation of A.
Option (B) is wrong because R is the explanation. Option (C) is wrong because R is not false. Option (D) is wrong because both statements are true.

Final Answer:
Both A and R are true, and R correctly explains A. This is option (A). \[ \boxed{\text{(A)}} \]