Consider the following statements. A, B and identify the correct choice in the given answers
(A) Density of a nucleus is independent of its mass number
(B) Beryllium is used as moderator in nuclear reactors

Options

A. A and B are correct
B. A and B are wrong
C. A is correct, B is wrong
D. A is wrong, B is correct

Answer

To solve the question regarding the statements A and B, we will analyze each statement step by step.

### Step 1: Analyze Statement A
**Statement A:** "Density of a nucleus is independent of its mass number."

1. **Understanding Density:** Density (ρ) is defined as mass (m) divided by volume (V). Mathematically, it can be expressed as:
\[ \rho = \frac{m}{V} \]

2. **Mass of the Nucleus:** The mass of a nucleus is approximately proportional to its mass number (A), since the mass number is the total number of protons and neutrons in the nucleus. Thus, we can say:
\[ m \propto A \]

3. **Volume of the Nucleus:** The volume of a nucleus can be approximated using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where the radius (r) of the nucleus is given by:
\[ r = r_0 A^{1/3} \]
Here, \( r_0 \) is a constant.

4. **Substituting the Radius into Volume:** By substituting the expression for r into the volume formula, we get:
\[ V = \frac{4}{3} \pi (r_0 A^{1/3})^3 = \frac{4}{3} \pi r_0^3 A \]

5. **Calculating Density:** Now substituting mass and volume into the density formula:
\[ \rho = \frac{A}{\frac{4}{3} \pi r_0^3 A} = \frac{3}{4 \pi r_0^3} \]
Notice that the mass number A cancels out.

6. **Conclusion for Statement A:** The density of the nucleus is indeed independent of its mass number. Therefore, Statement A is **True**.

### Step 2: Analyze Statement B
**Statement B:** "Beryllium is used as a moderator in nuclear reactors."

1. **Understanding Moderators:** In nuclear reactors, moderators are materials used to slow down the neutrons produced during fission reactions, allowing for a sustained chain reaction.

2. **Commonly Used Moderators:** Common materials used as moderators include water, heavy water, and graphite. Beryllium is also known to be used as a moderator due to its ability to slow down neutrons effectively.

3. **Conclusion for Statement B:** Beryllium is indeed used as a moderator in some types of nuclear reactors. Therefore, Statement B is **True**.

### Final Conclusion
Both statements A and B are correct. Therefore, the correct choice is that both statements are true.

### Summary of the Solution:
- Statement A is True: Density of a nucleus is independent of its mass number.
- Statement B is True: Beryllium is used as a moderator in nuclear reactors.
- The correct answer is that both statements A and B are correct.

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