Calculate the unceertainty in the momentum of a particle if the uncertainity in its position is ` 6.6 xx 10^(-32) m `

Explanation

To calculate the uncertainty in momentum (Δp) of a particle given the uncertainty in its position (Δx), we will use Heisenberg's Uncertainty Principle, which states:

\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]

Where:
- Δx is the uncertainty in position,
- Δp is the uncertainty in momentum,
- h is Planck's constant, approximately \(6.625 \times 10^{-34} \, \text{Joule second}\).

### Step-by-step solution:

1. **Identify the given values**:
- Uncertainty in position, \( \Delta x = 6.6 \times 10^{-32} \, \text{m} \)
- Planck's constant, \( h = 6.625 \times 10^{-34} \, \text{Joule second} \)

2. **Use the formula to express Δp**:
\[ \Delta p = \frac{h}{4\pi \Delta x} \]

3. **Substitute the known values into the formula**:
\[ \Delta p = \frac{6.625 \times 10^{-34}}{4 \times 3.14 \times 6.6 \times 10^{-32}} \]

4. **Calculate the denominator**:
- First, calculate \( 4 \times 3.14 \):
\[ 4 \times 3.14 = 12.56 \]
- Now multiply by \( 6.6 \times 10^{-32} \):
\[ 12.56 \times 6.6 \approx 82.956 \quad \text{(keeping significant figures in mind)} \]

5. **Combine the powers of ten**:
\[ \Delta p = \frac{6.625 \times 10^{-34}}{82.956 \times 10^{-32}} = \frac{6.625}{82.956} \times 10^{-34 + 32} \]

6. **Calculate the numerical value**:
\[ \Delta p \approx 0.0799 \times 10^{-2} \, \text{kg m/s} \]

7. **Express in scientific notation**:
\[ \Delta p \approx 8.0 \times 10^{-4} \, \text{kg m/s} \]

### Final Answer:
The uncertainty in momentum (Δp) is approximately \( 8.0 \times 10^{-4} \, \text{kg m/s} \).