A: K.E of two subatomic particles having same De - Broglie 's wavelength is same
R : de - Broglie 's wavelength is directly related to mass of subatomic particles

Options

A. IF both assertion & reason are true and the reason is the correct explanation of the assertion then mark
B. IF both assertion & reason are true but the reason is not the correct explanation of the assertion , then mark
C. IF assertion is true statement but reason is false , then mark
D. If both assertion and reason are false statements then mark

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the kinetic energy (K.E) of two subatomic particles having the same de Broglie wavelength is the same.
- According to the de Broglie hypothesis, the momentum \( p \) of a particle is given by the formula:
\[ p = \frac{h}{\lambda} \]
where \( h \) is Planck's constant and \( \lambda \) is the de Broglie wavelength.

2. **Analyzing the Kinetic Energy**:
- The kinetic energy of a particle is given by the formula:
\[ K.E = \frac{p^2}{2m} \]
where \( m \) is the mass of the particle.
- If two particles have the same de Broglie wavelength, their momentum \( p \) will be the same because \( p = \frac{h}{\lambda} \) and \( \lambda \) is constant for both particles.

3. **Dependence on Mass**:
- Since \( p \) is the same for both particles, the kinetic energy will depend on their masses:
\[ K.E = \frac{p^2}{2m} \]
- Therefore, if the masses of the two particles are different, their kinetic energies will also be different. Hence, the assertion is **false**.

4. **Understanding the Reason (R)**:
- The reason states that de Broglie's wavelength is directly related to the mass of subatomic particles.
- From the de Broglie equation, we can derive:
\[ \lambda = \frac{h}{mv} \]
- This shows that the de Broglie wavelength is inversely proportional to the mass (and velocity) of the particle. Therefore, the statement that it is directly related to mass is also **false**.

5. **Conclusion**:
- Both the assertion (A) and the reason (R) are false statements.
- Therefore, the correct answer to the question is option 4: Both assertion and reason are false.