The uncertainity in the momentum of an electron is `1.0xx10^(-5)"kg m s"^(-1)`. The uncertainity in its position will be: `(h=6.626xx10^(-34)Js)`

Options

A. `1.05 xx 10^(-28)m`
B. `1.05 xx 10^(-26)m`
C. `5.27xx10^(-30)m`
D. `5.25xx10^(-28)m`

Explanation

To find the uncertainty in the position of an electron given the uncertainty in its momentum, we can use the Heisenberg Uncertainty Principle. The principle states that:

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

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

Given:
- \(\Delta p = 1.0 \times 10^{-5} \, \text{kg m/s}\)

We need to find \(\Delta x\).

### Step 1: Rearranging the Heisenberg Uncertainty Principle
From the Heisenberg Uncertainty Principle, we can rearrange the formula to solve for \(\Delta x\):

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

### Step 2: Substitute the Values
Now, we will substitute the known values into the equation:

\[ \Delta x \geq \frac{6.626 \times 10^{-34} \, \text{Js}}{4 \cdot \pi \cdot (1.0 \times 10^{-5} \, \text{kg m/s})} \]

### Step 3: Calculate the Denominator
First, calculate the denominator:

\[ 4 \cdot \pi \cdot (1.0 \times 10^{-5}) \approx 4 \cdot 3.14 \cdot 1.0 \times 10^{-5} \approx 1.256 \times 10^{-4} \]

### Step 4: Calculate \(\Delta x\)
Now, substitute this value back into the equation for \(\Delta x\):

\[ \Delta x \geq \frac{6.626 \times 10^{-34}}{1.256 \times 10^{-4}} \approx 5.27 \times 10^{-30} \, \text{m} \]

### Conclusion
Thus, the uncertainty in the position of the electron is approximately:

\[ \Delta x \geq 5.27 \times 10^{-30} \, \text{m} \]