The uncertainty in the momentum of a particle is `3.3 xx10^(-2) kg ms^(-1)` the uncertainty in its position will be

Options

A. `1.6 xx 10^(-33)`m
B. `1.6 xx 10^(-32)`m
C. `1.6 xx 10^(-30)`m
D. `1.6 xx 10^(-29)`m

Answer

To find the uncertainty in the position of a particle given the uncertainty in its momentum, we will apply Heisenberg's Uncertainty Principle. The principle states:

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

Where:
- \(\Delta x\) is the uncertainty in position,
- \(\Delta p\) is the uncertainty in momentum,
- \(h\) is Planck's constant, approximately \(6.626 \times 10^{-34} \, \text{J s}\),
- \(\pi\) is approximately \(3.14\).

### Step-by-step Solution:

1. **Identify the given values**:
- Uncertainty in momentum (\(\Delta p\)) = \(3.3 \times 10^{-2} \, \text{kg m/s}\)
- Planck's constant (\(h\)) = \(6.626 \times 10^{-34} \, \text{J s}\)
- Value of \(\pi\) = \(3.14\)

2. **Rearrange Heisenberg's Uncertainty Principle**:
We need to find \(\Delta x\), so we rearrange the formula:
\[ \Delta x \geq \frac{h}{4\pi \Delta p} \]

3. **Substitute the known values into the equation**:
\[ \Delta x \geq \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times (3.3 \times 10^{-2})} \]

4. **Calculate the denominator**:
- First, calculate \(4 \times 3.14\):
\[ 4 \times 3.14 = 12.56 \]
- Now calculate \(12.56 \times (3.3 \times 10^{-2})\):
\[ 12.56 \times 3.3 \times 10^{-2} = 0.41568 \approx 0.416 \]

5. **Complete the calculation for \(\Delta x\)**:
\[ \Delta x \geq \frac{6.626 \times 10^{-34}}{0.416} \]
- Now perform the division:
\[ \Delta x \geq 1.59 \times 10^{-33} \, \text{m} \]

6. **Final result**:
Rounding off, we can express the uncertainty in position as:
\[ \Delta x \geq 1.6 \times 10^{-33} \, \text{m} \]

### Conclusion:
The uncertainty in the position of the particle is approximately \(1.6 \times 10^{-33} \, \text{m}\).