Band gap in germanium is small.
The energy spread of each germanium atomic energy level is infinitesimally small.

Options

A. If both assertion and reason are correct and reason is correct explanation for assertion
B. If both assertion and reason are correct but reason is not correct explanation for assertion
C. If assertion is correct but reason is incorrect
D. If both assertion and reason are incorrect

Explanation

To solve the question regarding the small band gap in germanium and the infinitesimally small energy spread of its atomic energy levels, we can break down the solution into clear steps:

### Step-by-Step Solution

1. **Understanding the Assertion**: The assertion states that the band gap in germanium is small. This is true because germanium is classified as a semiconductor.

**Hint**: Recall the definition of semiconductors and their characteristic properties.

2. **Understanding the Band Gap**: The band gap refers to the energy difference between the valence band (where electrons are normally present) and the conduction band (where electrons can move freely to conduct electricity). In semiconductors like germanium, this gap is small, allowing electrons to easily jump from the valence band to the conduction band.

**Hint**: Consider the energy levels of electrons in solids and how they relate to electrical conductivity.

3. **Understanding the Reason**: The reason states that the energy spread of each germanium atomic energy level is infinitesimally small. This is also correct. In germanium, the energy levels are closely spaced, which contributes to the small band gap.

**Hint**: Think about how atomic energy levels are structured in solids and how this affects their conductivity.

4. **Calculating the Energy of One Atomic Level**: The band gap in germanium is approximately 64 kJ/mol. To find the energy of a single atomic level, we divide this value by Avogadro's number (6.022 x 10^23 atoms/mol):

\[ \text{Energy of one atomic level} = \frac{64 \text{ kJ/mol}}{6.022 \times 10^{23} \text{ atoms/mol}} \approx 10.62 \times 10^{-23} \text{ J} \]

**Hint**: Remember to convert kJ to J when performing calculations.

5. **Interpreting the Result**: The calculated energy of one atomic level (10.62 x 10^-23 J) is indeed very small, indicating that the energy spread of each atomic energy level is infinitesimally small.

**Hint**: Consider the implications of having small energy levels on the behavior of electrons in a semiconductor.

6. **Conclusion**: Both the assertion and reason are correct. However, the reason provided does not serve as the correct explanation for the assertion. The small band gap is primarily due to germanium being a semiconductor, not solely because of the small energy spread of atomic levels.

**Hint**: Reflect on the relationship between the properties of materials and their classification as conductors, semiconductors, or insulators.

### Final Answer
Both the assertion and reason are correct, but the reason is not the correct explanation for the assertion. Thus, the correct answer is that both statements are true, but the reason does not explain the assertion.