(A): All the intrinsic semiconductors are insulators at absolute zero
(R): All electrons are tightly bound at absolute zero.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. 'A' is true and 'R' is false
D. 'A' is false and 'R' is true

Answer

To analyze the given statements, we will evaluate the assertion (A) and the reason (R) step by step.

### Step 1: Understanding the Assertion
**Assertion (A): All the intrinsic semiconductors are insulators at absolute zero.**

- **Explanation**: At absolute zero (0 Kelvin), the thermal energy available to the electrons in a semiconductor is zero. In intrinsic semiconductors, there is a small energy gap (band gap) between the valence band (where electrons are present) and the conduction band (where electrons can move freely and conduct electricity). At absolute zero, electrons do not have enough energy to overcome this band gap and transition from the valence band to the conduction band. As a result, they cannot contribute to electrical conduction, making the intrinsic semiconductors behave like insulators.

### Step 2: Understanding the Reason
**Reason (R): All electrons are tightly bound at absolute zero.**

- **Explanation**: This statement is also true. At absolute zero, electrons in the valence band of a semiconductor are in their lowest energy state and are tightly bound to their respective atoms. Since there is no thermal energy to excite these electrons to the conduction band, they remain bound and do not contribute to electrical conduction. This tightly bound state of electrons is what prevents conduction in intrinsic semiconductors at absolute zero.

### Step 3: Conclusion
Both the assertion and the reason are true. Furthermore, the reason correctly explains the assertion. Therefore, the correct answer is that both A and R are true, and R is the correct explanation of A.

### Final Answer:
Both the assertion (A) and the reason (R) are true, and R is the correct explanation of A.

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