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 in the question.

### 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.
- The formula for kinetic energy is given by:
\[ K.E = \frac{1}{2} mv^2 \]
- The de Broglie wavelength (λ) is given by:
\[ \lambda = \frac{h}{mv} \]
where \( h \) is Planck's constant, \( m \) is the mass of the particle, and \( v \) is its velocity.

2. **Relating K.E and de Broglie Wavelength**:
- Rearranging the de Broglie wavelength formula gives:
\[ mv = \frac{h}{\lambda} \]
- Substituting \( mv \) into the kinetic energy formula:
\[ K.E = \frac{1}{2} m \left(\frac{h}{m\lambda}\right)^2 = \frac{h^2}{2m\lambda^2} \]
- This shows that kinetic energy is inversely proportional to the mass \( m \) when the wavelength \( \lambda \) is constant.

3. **Analyzing the Kinetic Energy for Different Particles**:
- If we take two different subatomic particles (e.g., an electron and a proton) with the same de Broglie wavelength, they will have different masses.
- Since kinetic energy is inversely proportional to mass, the kinetic energies of the two particles cannot be the same if their masses are different.
- Therefore, the assertion (A) is **false**.

4. **Understanding the Reason (R)**:
- The reason states that de Broglie's wavelength is directly related to the mass of subatomic particles.
- However, from the de Broglie wavelength formula, we see that:
\[ \lambda \propto \frac{1}{m} \]
- This indicates that the wavelength is **inversely** related to mass, not directly related.
- Therefore, the reason (R) is also **false**.

5. **Conclusion**:
- Both the assertion (A) and the reason (R) are false.
- Hence, the correct option is **D**: Both assertion and reason are false.