For a certain particle, it is found that uncertainty in velocity is reciprocal of uncertainty in position. This implies that

Options

A. Mass of the particle is `gt` unity
B. Mass of the particle is unity
C. Mass of the particle `le` h
D. Mass of the particle `ge h//4 pi`.

Explanation

To solve the problem, we need to analyze the relationship between the uncertainties in velocity and position as given in the question.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We are given that the uncertainty in velocity (Δv) is the reciprocal of the uncertainty in position (Δx). Mathematically, this can be expressed as:
\[ \Delta v \propto \frac{1}{\Delta x} \]
This implies:
\[ \Delta v \cdot \Delta x = k \]
where \( k \) is a constant.

2. **Applying Heisenberg's Uncertainty Principle**:
According to Heisenberg's Uncertainty Principle, the product of the uncertainties in position and momentum is given by:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
where \( \Delta p \) is the uncertainty in momentum and \( h \) is Planck's constant.

3. **Relating Momentum to Mass and Velocity**:
The uncertainty in momentum (Δp) can be expressed as:
\[ \Delta p = m \cdot \Delta v \]
where \( m \) is the mass of the particle.

4. **Substituting into the Uncertainty Principle**:
Now substituting \( \Delta p \) into the uncertainty principle:
\[ \Delta x \cdot (m \cdot \Delta v) \geq \frac{h}{4\pi} \]
From our earlier relationship, we have \( \Delta v = \frac{k}{\Delta x} \). Substituting this into the equation gives:
\[ \Delta x \cdot \left(m \cdot \frac{k}{\Delta x}\right) \geq \frac{h}{4\pi} \]
Simplifying this, we get:
\[ m \cdot k \geq \frac{h}{4\pi} \]

5. **Finding the Condition on Mass**:
Rearranging the inequality gives:
\[ m \geq \frac{h}{4\pi k} \]
Since \( k \) is a constant, we can denote it as \( k = 1 \) for simplicity, which leads to:
\[ m \geq \frac{h}{4\pi} \]

6. **Conclusion**:
From the above derivation, we conclude that the mass of the particle must be greater than \( \frac{h}{4\pi} \). Thus, the correct answer is:
- The mass of the particle is greater than \( \frac{h}{4\pi} \).

### Final Answer:
The mass of the particle is greater than \( \frac{h}{4\pi} \).