If uncertainty in position and momentum are equal then uncertainty in velocity is.

Options

A. `sqrt((h)/(pi))`
B. `sqrt((h)/(2 pi))`
C. `(1)/(2m) sqrt((h)/(pi))`
D. None of these

Explanation

To solve the problem, we need to find the uncertainty in velocity (Δv) given that the uncertainty in position (Δx) and the uncertainty in momentum (Δp) are equal.

### Step-by-Step Solution:

1. **Understand the Given Information**:
We are given that:
\[ \Delta x = \Delta p \]
where Δx is the uncertainty in position and Δp is the uncertainty in momentum.

2. **Recall the Uncertainty Principle**:
According to Heisenberg's uncertainty principle:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
where h is Planck's constant.

3. **Substitute Δp**:
Since we know that Δp = mΔv (where m is mass and Δv is the uncertainty in velocity), we can write:
\[ \Delta x \cdot m \Delta v \geq \frac{h}{4\pi} \]

4. **Express Δv in terms of Δx**:
We can rearrange the equation to find Δv:
\[ m \Delta v \geq \frac{h}{4\pi \Delta x} \]
Therefore,
\[ \Delta v \geq \frac{h}{4\pi m \Delta x} \]

5. **Using the Given Condition**:
Since Δx = Δp, we can replace Δp in our equation:
\[ \Delta v \geq \frac{h}{4\pi m \Delta p} \]

6. **Final Expression**:
Thus, we can conclude that the uncertainty in velocity (Δv) is:
\[ \Delta v = \frac{h}{4\pi m \Delta x} \]

### Conclusion:
The uncertainty in velocity (Δv) can be expressed in terms of the uncertainty in position (Δx) and the mass (m) of the particle.