If `m,m_n` and `m_p` are masses of `._Z X^A` nucleus, neutron and proton respectively.

Options

A. `m=(A-Z)m_n+Zm_p`
B. `m=(A-Z)m_p+Zm_n`
C. `m lt (A-Z) m_n+Zm_p`
D. `m gt (A-Z) m_n+Zm_p`

Answer

To solve the problem, we need to understand the relationship between the masses of the nucleus, protons, and neutrons, and how mass defect plays a role in this relationship.

### Step-by-Step Solution:

1. **Identify the Components of the Nucleus**:
- The nucleus of an element \( _Z X^A \) contains \( Z \) protons and \( A - Z \) neutrons.

2. **Calculate the Theoretical Mass of the Nucleus**:
- The theoretical mass of the nucleus can be calculated using the masses of protons and neutrons:
\[ M_{theoretical} = Z \cdot m_p + (A - Z) \cdot m_n \]
- Here, \( m_p \) is the mass of a proton and \( m_n \) is the mass of a neutron.

3. **Experimental Mass of the Nucleus**:
- The experimental mass of the nucleus is denoted as \( m \).

4. **Understanding Mass Defect**:
- The mass defect occurs due to the binding energy of the nucleus. The binding energy is the energy required to disassemble the nucleus into its constituent protons and neutrons.
- Due to this binding energy, the experimental mass \( m \) of the nucleus is less than the theoretical mass \( M_{theoretical} \):
\[ m < M_{theoretical} \]

5. **Conclusion**:
- Therefore, we can conclude that the experimental mass \( m \) is less than the sum of the masses of the individual protons and neutrons that make up the nucleus. This leads us to the correct option in the context of the question.

### Final Statement:
The correct relationship is:
\[ m < Z \cdot m_p + (A - Z) \cdot m_n \]
Thus, the answer is option number three.

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