Assertion: A particle of mass `M` at rest decays into two particles of masses `m_(1)` and `m_(2)`, having non-zero velocities will have ratio of the de-broglie wavelength unity.
Reason: Here we cannot apply conservation of linear momentum.

Options

A. If both Assertion and Reason are true and Reason is correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If both Assertion and Reason are false.

Answer

To solve the problem, we need to analyze both the assertion and the reason provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that a particle of mass \( M \) at rest decays into two particles of masses \( m_1 \) and \( m_2 \) with non-zero velocities, and that the ratio of their de Broglie wavelengths is unity.

2. **Initial Conditions**:
- The initial momentum of the system is zero since the particle is at rest. Thus, we have:
\[ p_{\text{initial}} = 0 \]

3. **Final Momentum**:
- After the decay, the two particles will have velocities \( v_1 \) and \( v_2 \). The final momentum can be expressed as:
\[ p_{\text{final}} = m_1 v_1 + m_2 v_2 \]

4. **Applying Conservation of Momentum**:
- According to the conservation of momentum:
\[ p_{\text{initial}} = p_{\text{final}} \implies 0 = m_1 v_1 + m_2 v_2 \]
- Rearranging gives:
\[ m_1 v_1 = -m_2 v_2 \]

5. **Taking Magnitudes**:
- Taking the magnitudes of both sides, we have:
\[ m_1 |v_1| = m_2 |v_2| \]

6. **De Broglie Wavelength**:
- The de Broglie wavelength \( \lambda \) is given by:
\[ \lambda = \frac{h}{mv} \]
- Therefore, for the two particles, we have:
\[ \lambda_1 = \frac{h}{m_1 v_1} \quad \text{and} \quad \lambda_2 = \frac{h}{m_2 v_2} \]

7. **Finding the Ratio of Wavelengths**:
- The ratio of the de Broglie wavelengths is:
\[ \frac{\lambda_1}{\lambda_2} = \frac{m_2 v_2}{m_1 v_1} \]
- Substituting \( m_1 |v_1| = m_2 |v_2| \) into the equation gives:
\[ \frac{\lambda_1}{\lambda_2} = \frac{m_2 v_2}{m_1 v_1} = 1 \]
- Thus, the ratio of the de Broglie wavelengths is indeed unity.

8. **Analyzing the Reason**:
- The reason states that we cannot apply conservation of linear momentum. This is incorrect because we can apply conservation of momentum in this scenario since the initial momentum is zero and the system is closed.

9. **Conclusion**:
- The assertion is true (the ratio of de Broglie wavelengths is unity), while the reason is false (we can apply conservation of momentum).

### Final Answer:
- The correct option is: Assertion is true, but Reason is false.