Let `m_p` be the mass of a proton , `m_n` the mass of a neutron, `M_1` the mass of a `._10^20Ne` nucleus and `M_2` the mass of a `._20^40Ca` nucleus . Then

Options

A. `M_2 = M_1`
B. `M_2 gt M_1`
C. `M_2 lt 2M_1`
D. `M_1 lt 10 (m_n + m_p)`

Explanation

To solve the problem, we need to analyze the masses of the nuclei of Neon and Calcium based on their constituent protons and neutrons.

### Step-by-Step Solution:

1. **Identify the Composition of the Nuclei:**
- The nucleus of Neon-20 (\( _{10}^{20}Ne \)) consists of 10 protons and 10 neutrons.
- The nucleus of Calcium-40 (\( _{20}^{40}Ca \)) consists of 20 protons and 20 neutrons.

2. **Calculate the Theoretical Masses:**
- The theoretical mass of the Neon nucleus (\( M_1 \)) can be calculated as:
\[ M_1^{\text{theoretical}} = 10m_p + 10m_n \]
- The theoretical mass of the Calcium nucleus (\( M_2 \)) can be calculated as:
\[ M_2^{\text{theoretical}} = 20m_p + 20m_n \]

3. **Consider Mass Defect:**
- Due to the binding energy, the actual (experimental) mass of the nuclei is less than the theoretical mass. Therefore:
\[ M_1 < M_1^{\text{theoretical}} \quad \text{and} \quad M_2 < M_2^{\text{theoretical}} \]
- This implies:
\[ M_1 < 10m_p + 10m_n \quad \text{and} \quad M_2 < 20m_p + 20m_n \]

4. **Comparison of Masses:**
- Since both \( M_1 \) and \( M_2 \) are less than their respective theoretical masses, we can summarize:
\[ M_1 < 10m_p + 10m_n \quad \text{and} \quad M_2 < 20m_p + 20m_n \]
- However, we cannot directly compare \( M_1 \) and \( M_2 \) or their multiples without additional information.

5. **Conclusion:**
- The relationship between the masses does not allow for a direct comparison of \( M_1 \) and \( M_2 \) or their multiples. Thus, the correct conclusion is that the mass of the Neon nucleus is less than its theoretical mass, and the same applies to the Calcium nucleus.

### Final Answer:
The correct option is that \( M_1 < 10m_p + 10m_n \) and \( M_2 < 20m_p + 20m_n \), but we cannot establish a direct relationship between \( M_1 \) and \( M_2 \).