The uncertainty of a particle in momentum is `3.3xx10^(-2)" kg "ms^(-1)`. Calculate the uncertainty in its position.
`(h=6.6xx10^(-34)J-sec)`.

Answer

To solve the problem of calculating the uncertainty in position (Δx) given the uncertainty in momentum (Δp) and Planck's constant (h), we can use Heisenberg's uncertainty principle. Here’s the step-by-step solution:

### Step 1: Understand the Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle states that the product of the uncertainties in position (Δx) and momentum (Δp) is always greater than or equal to a constant value:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]

### Step 2: Rearrange the Formula
We want to find the uncertainty in position (Δx). Therefore, we can rearrange the formula to solve for Δx:
\[ \Delta x \geq \frac{h}{4\pi \Delta p} \]

### Step 3: Substitute the Given Values
We have:
- Planck's constant, \( h = 6.6 \times 10^{-34} \, \text{J-sec} \)
- Uncertainty in momentum, \( \Delta p = 3.3 \times 10^{-2} \, \text{kg m/s} \)

Now we can substitute these values into the rearranged formula:
\[ \Delta x \geq \frac{6.6 \times 10^{-34}}{4\pi (3.3 \times 10^{-2})} \]

### Step 4: Calculate the Denominator
First, calculate \( 4\pi \):
\[ 4\pi \approx 12.566 \]

Now, calculate the product:
\[ 4\pi \Delta p = 12.566 \times 3.3 \times 10^{-2} \]
\[ 4\pi \Delta p \approx 0.415 \]

### Step 5: Calculate Δx
Now substitute this back into the equation for Δx:
\[ \Delta x \geq \frac{6.6 \times 10^{-34}}{0.415} \]

Perform the division:
\[ \Delta x \geq 1.587 \times 10^{-33} \, \text{m} \]

### Step 6: Final Result
Thus, the uncertainty in position (Δx) is:
\[ \Delta x \geq 1.59 \times 10^{-33} \, \text{m} \]

### Summary
The uncertainty in the position of the particle is approximately \( 1.59 \times 10^{-33} \, \text{m} \).

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