An atom has mass of 0.01 kg and uncertainty in its velocity is 4.318×`10^(−6)`m/s then uncertainty in position is (h=6.626×`10^(−34)`Js)

Options

A. 7.2×`10^(−28)`m
B. 1.27×`10^(−27)`m
C. 2.2×`10^(−24)`m
D. None

Explanation

To find the uncertainty in position (Δx) of an atom given its mass and uncertainty in velocity, we can use the Heisenberg Uncertainty Principle, which is given by the formula:

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

Where:
- \( \Delta x \) = uncertainty in position
- \( m \) = mass of the atom
- \( \Delta v \) = uncertainty in velocity
- \( h \) = Planck's constant

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the atom, \( m = 0.01 \, \text{kg} \)
- Uncertainty in velocity, \( \Delta v = 4.318 \times 10^{-6} \, \text{m/s} \)
- Planck's constant, \( h = 6.626 \times 10^{-34} \, \text{Js} \)

2. **Substitute the Values into the Uncertainty Principle:**
Rearranging the formula to solve for \( \Delta x \):
\[ \Delta x \geq \frac{h}{4\pi m \Delta v} \]

3. **Calculate \( 4\pi \):**
Using \( \pi \approx 3.14 \):
\[ 4\pi \approx 4 \times 3.14 = 12.56 \]

4. **Substitute All Values into the Equation:**
\[ \Delta x \geq \frac{6.626 \times 10^{-34}}{12.56 \times 0.01 \times 4.318 \times 10^{-6}} \]

5. **Calculate the Denominator:**
\[ 12.56 \times 0.01 \times 4.318 \times 10^{-6} = 5.433 \times 10^{-7} \]

6. **Calculate \( \Delta x \):**
\[ \Delta x \geq \frac{6.626 \times 10^{-34}}{5.433 \times 10^{-7}} \approx 1.22 \times 10^{-27} \, \text{m} \]

### Final Result:
The uncertainty in position \( \Delta x \) is approximately \( 1.22 \times 10^{-27} \, \text{m} \).