which of the following is the correct expression for a Heisenberg's uncertainty principle?

Options

A. `Deltax`. `Deltap ge h/4π`
B. `Deltax. Deltap ge h/2π`
C. `Deltax. Deltap le h/4π`
D. `Deltax. Deltap =h/(sqrt2π)`

Answer

To solve the question regarding the correct expression for Heisenberg's uncertainty principle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Heisenberg Uncertainty Principle**:
The Heisenberg Uncertainty Principle states that it is impossible to simultaneously know both the position (x) and momentum (p) of a particle with absolute precision. The principle can be mathematically expressed as:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
where:
- \(\Delta x\) = uncertainty in position
- \(\Delta p\) = uncertainty in momentum
- \(h\) = Planck's constant

2. **Identify the Variables**:
In this expression:
- \(\Delta x\) represents the uncertainty in the position of the particle.
- \(\Delta p\) represents the uncertainty in the momentum of the particle.

3. **Check the Given Options**:
We need to evaluate the provided options to find which one matches the Heisenberg Uncertainty Principle expression.

- **Option 1**: \(\Delta x \cdot \Delta p \geq \frac{h}{4\pi}\) (This matches the principle)
- **Option 2**: \(\Delta x \cdot \Delta p \geq \frac{h}{2}\) (This does not match)
- **Option 3**: \(\Delta x \cdot \Delta p \leq \frac{h}{2}\) (This does not match)
- **Option 4**: (Not provided in the transcript, but we can assume it does not match)

4. **Conclusion**:
Based on the evaluation, the correct expression that represents Heisenberg's uncertainty principle is:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
Therefore, **Option 1** is the correct answer.