If `m_(p)` is the mass of proton. `m_(n)` that of a neutron, `M_(1)` that of `_(10)Ne^(20)` nucleus and `M_(2)` that of `_(20)Ca^(40)` nucleus, then which of the following relations is//are not true?

Options

A. `M_(2) gt 2M_(1)`
B. `M_(2) lt 20 (m_(p)+m_(n))`
C. `M_(2)=2M_(1)`
D. `M_(2) lt 2M_(1)`

Explanation

To solve the problem, we need to analyze the mass relations of the given nuclei and understand how binding energy affects the mass of a nucleus.

### Step-by-Step Solution:

1. **Understand the Mass of Nuclei**:
- The mass of a nucleus is generally less than the sum of the masses of its individual nucleons (protons and neutrons) due to the binding energy that holds the nucleus together. This phenomenon is known as mass defect.

2. **Define the Masses**:
- Let \( m_p \) be the mass of a proton.
- Let \( m_n \) be the mass of a neutron.
- The mass of the \( _{10}^{20}Ne \) nucleus is denoted as \( M_1 \).
- The mass of the \( _{20}^{40}Ca \) nucleus is denoted as \( M_2 \).

3. **Calculate the Expected Masses**:
- For the \( _{10}^{20}Ne \) nucleus, it has 10 protons and 10 neutrons, so the expected mass (without binding energy) would be:
\[ 10m_p + 10m_n = 10(m_p + m_n) \]
- For the \( _{20}^{40}Ca \) nucleus, it has 20 protons and 20 neutrons, so the expected mass would be:
\[ 20m_p + 20m_n = 20(m_p + m_n) \]

4. **Apply the Binding Energy Concept**:
- The actual mass of the nucleus will be less than the calculated expected mass due to binding energy:
\[ M_1 < 10(m_p + m_n) \]
\[ M_2 < 20(m_p + m_n) \]

5. **Compare the Nuclei**:
- Since \( _{20}^{40}Ca \) has more nucleons than \( _{10}^{20}Ne \), it will have a greater binding energy, leading to a larger mass defect. Thus:
\[ M_2 < 20m_p + 20m_n \]
- However, we can also infer that:
\[ M_2 < 2M_1 \]
- This is because the binding energy per nucleon generally increases with the number of nucleons, leading to a greater mass defect.

6. **Identify Incorrect Relations**:
- We need to check which of the proposed relations are not true based on the above deductions.

### Conclusion:
- The relations that are not true based on our analysis are:
- A: \( M_2 > 2M_1 \) (not true)
- C: \( M_1 > 10m_p + 10m_n \) (not true)

Thus, the incorrect options are A and C.