Assertion (A) : de-Broglie equation is significant for microscopic particles.
Reason (R ): de -Broglie wavelength is inversely proportional to the mass of a particle when velocity is kept constant.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is true

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "de-Broglie equation is significant for microscopic particles."
- The de-Broglie equation relates the wavelength (λ) of a particle to its momentum (p) through the formula:
\[ \lambda = \frac{h}{p} \]
- Here, \(h\) is Planck's constant, and \(p\) is the momentum of the particle.

2. **Understanding the Reason (R)**:
- The reason states that "de-Broglie wavelength is inversely proportional to the mass of a particle when velocity is kept constant."
- We can express momentum as:
\[ p = mv \]
- Substituting this into the de-Broglie equation gives:
\[ \lambda = \frac{h}{mv} \]
- From this equation, we see that if the velocity (v) is constant, then the wavelength (λ) is indeed inversely proportional to the mass (m) of the particle:
\[ \lambda \propto \frac{1}{m} \]

3. **Analyzing the Significance for Microscopic Particles**:
- For microscopic particles (like electrons), the mass is very small. Therefore, when the mass decreases, the wavelength increases significantly.
- This means that the wave-like behavior of these particles becomes more pronounced and significant, which is why the de-Broglie equation is particularly relevant for microscopic particles.

4. **Conclusion**:
- Both the assertion and the reason are true. The reason correctly explains why the assertion holds true. Therefore, we conclude that:
- Both A and R are true, and R is the correct explanation of A.

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