A : If a stationary nucleus emits an ` alpha` -perticle , the de Broglie wavelengths of te daugther nucleus and the ` alpha`-perticle and equal .
R : The magnitudes of the linear moments of the daughter nucleus and the `alpha`-perticle are the same .

Options

A. If both Assertion & Reason are ture and the reason is the correct explanation of the assertion , then mark (1) .
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion , then mark (2) .
C. If Assertion is true statement but Reason is false , then mark (3)
D. If both Assertion and Reason are false statements , then mark (4) .

Answer

To solve the problem, we need to analyze the two statements provided:

**Assertion (A)**: If a stationary nucleus emits an alpha particle, the de Broglie wavelengths of the daughter nucleus and the alpha particle are equal.

**Reason (R)**: The magnitudes of the linear momenta of the daughter nucleus and the alpha particle are the same.

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- We start with a stationary nucleus, which means its initial momentum is zero. When it emits an alpha particle, the total momentum before emission must equal the total momentum after emission due to the conservation of momentum.

2. **Applying Conservation of Momentum**:
- Let \( p_{\alpha} \) be the momentum of the emitted alpha particle and \( p_d \) be the momentum of the daughter nucleus.
- According to the conservation of momentum:
\[ 0 = p_{\alpha} + p_d \]
- This implies:
\[ p_{\alpha} = -p_d \]
- Therefore, the magnitudes of the momenta are equal:
\[ |p_{\alpha}| = |p_d| \]

3. **Relating Momentum to de Broglie Wavelength**:
- The de Broglie wavelength \( \lambda \) is given by the formula:
\[ \lambda = \frac{h}{p} \]
- For the alpha particle:
\[ \lambda_{\alpha} = \frac{h}{p_{\alpha}} \]
- For the daughter nucleus:
\[ \lambda_d = \frac{h}{p_d} \]
- Since \( |p_{\alpha}| = |p_d| \), we can write:
\[ \lambda_{\alpha} = \lambda_d \]

4. **Conclusion about the Statements**:
- Since we have shown that the de Broglie wavelengths of the daughter nucleus and the alpha particle are equal, the assertion (A) is true.
- We also established that the magnitudes of their momenta are equal, making the reason (R) true as well.

5. **Final Evaluation**:
- Both statements A and R are true. Moreover, R provides a correct explanation for A, as the equality of the momenta leads directly to the equality of the de Broglie wavelengths.

### Final Answer:
Both Assertion (A) and Reason (R) are true, and R is the correct explanation for A.