It is impossible to determine simultaneously the position of velocity of small microscopic particle such as electron , proton or neutron with accuracy .This is called Heisenberg's uncertainty principle. Mathematically, it is represented as `Delta x. Delta p ge (h)/(4pi) , Delta x` is uncertainty in position `Delta p ` is uncertainty in momentum.

Options

A. `5.28 xx 10^(-30)m`
B. `2.64 xx 10^(-30)m`
C. `1.30 xx 10^(-30)m`
D. `0.66 xx 10^(-30)m`

Explanation

To solve the problem related to Heisenberg's Uncertainty Principle, we will follow these steps:

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

### Step 2: Identify the constants
In this equation:
- \( h \) is Planck's constant, which has a value of \( 6.626 \times 10^{-34} \, \text{Js} \).
- \( \pi \) is a mathematical constant approximately equal to \( 3.14 \).

### Step 3: Calculate \( 4\pi \)
We need to calculate \( 4\pi \):
\[ 4\pi = 4 \times 3.14 = 12.56 \]

### Step 4: Substitute the values into the formula
Now, substitute the value of \( h \) and \( 4\pi \) into the equation:
\[ \Delta x \cdot \Delta p \geq \frac{6.626 \times 10^{-34}}{12.56} \]

### Step 5: Perform the division
Now, we will perform the division:
\[ \Delta x \cdot \Delta p \geq \frac{6.626 \times 10^{-34}}{12.56} \approx 5.28 \times 10^{-35} \]

### Step 6: Conclusion
Thus, the uncertainty in position and momentum must satisfy:
\[ \Delta x \cdot \Delta p \geq 5.28 \times 10^{-35} \]

### Final Answer
The value of \( \Delta x \cdot \Delta p \) is at least \( 5.28 \times 10^{-35} \).

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