Question

Direction: Question consists of two statements, one labeled as the 'Assertion (A)' and the other as 'Reason (R)'. Examine these two statements carefully and select the answer to this question using the codes given below:

Assertion (A): In an intrinsic semiconductor, the concentration of electrons and holes increases with an increase in temperature.

Reason (R): Law of mass action holds good in the case of semiconductors.

1. Both A and R are individually true and R is the correct explanation of A
2. Both A and R are individually true but R is not the correct explanation of A
3. A is true but R is false
4. A is false but R is true

Answer 1

Correct Answer - Option 2 : Both A and R are individually true but R is not the correct explanation of A

Explanation-

In electronics and semiconductor physics, the law of mass action is a relation between the concentrations of free electrons and electron holes under thermal equilibrium.

It states that, under thermal equilibrium, the product of the free electron concentration {n} and the free hole concentration {p} is equal to a constant square of intrinsic carrier concentration. The intrinsic carrier concentration is a function of temperature.

From Mass Action law:

\(np = n_i^2\)

Where, n_i = intrinsic carrier concentration

n = tree electron concentration

p = hole concentration

\(n_i^2 = {A_0}{T^3}{e^{\frac{{ - Eg}}{{KT}}}}\)

\(n_i^2 \propto {T^3}\)

\({n_i} \propto {T^{\frac{3}{2}}}\)

For intrinsic semiconductor n = p = n_i

Hence,

 \(\left. {\begin{array}{*{20}{c}} {n \propto {T^{\frac{3}{2}}}}\\ {p \propto {T^{\frac{3}{2}}}} \end{array}} \right\}\)

So on increasing temperature free e^- and hole concentration will increase in an intrinsic semiconductor

So both statements are true but R is not the correct explanation of A.