`M_n` and `M_p` represent mass of neutron and proton respectively. If an element having atomic mass `M` has `N-`neutron and `Z`-proton, then the correct relation will be :

Options

A. `M lt {N.M_n+Z.M_p}`
B. `M gt {N.M_n+Z.M_p}`
C. `M = {N.M_n+Z.M_p}`
D. `M = N{M_n+M_p}`

Answer

To solve the problem, we need to establish the relationship between the atomic mass \( M \), the number of neutrons \( N \), and the number of protons \( Z \) in an element, considering the masses of neutrons and protons.

### Step-by-Step Solution:

1. **Identify the Masses**:
- Let \( M_n \) be the mass of a neutron.
- Let \( M_p \) be the mass of a proton.

2. **Define the Total Mass of Nucleons**:
- The total mass of nucleons (which includes both protons and neutrons) can be expressed as:
\[ \text{Total Mass of Nucleons} = Z \cdot M_p + N \cdot M_n \]
where \( Z \) is the number of protons and \( N \) is the number of neutrons.

3. **Relate to Atomic Mass**:
- The actual atomic mass \( M \) of the element is generally less than the total mass of nucleons due to the binding energy that holds the nucleus together. This can be expressed as:
\[ M < Z \cdot M_p + N \cdot M_n \]

4. **Understanding Mass Defect**:
- The difference between the total mass of the nucleons and the actual mass \( M \) is known as the mass defect, which is related to the binding energy of the nucleus. The binding energy is the energy required to hold the nucleus together, and it accounts for the mass lost during the formation of the nucleus.

5. **Final Relation**:
- Therefore, the correct relation that describes the relationship between the atomic mass \( M \), the number of neutrons \( N \), and the number of protons \( Z \) is:
\[ M < Z \cdot M_p + N \cdot M_n \]

### Conclusion:
The correct relation is that the atomic mass \( M \) is less than the total mass of the nucleons, which is given by \( Z \cdot M_p + N \cdot M_n \).