If the uncertainty in the position of an electron is zero the uncertainty in its momentum be

Options

A. zero
B. Greater than `(h)/( 4 pi)`
C. Less than `(h)/( 4 pi)`
D. infinite

Answer

To solve the question regarding the uncertainty in the momentum of an electron when the uncertainty in its position is zero, 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 the exact position and momentum of a particle. Mathematically, it is expressed as:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
where \(\Delta x\) is the uncertainty in position and \(\Delta p\) is the uncertainty in momentum.

2. **Set the Uncertainty in Position**:
In this scenario, we are given that the uncertainty in the position of the electron (\(\Delta x\)) is zero:
\[ \Delta x = 0 \]

3. **Substitute into the Uncertainty Principle**:
Substitute \(\Delta x = 0\) into the Heisenberg Uncertainty Principle equation:
\[ 0 \cdot \Delta p \geq \frac{h}{4\pi} \]
This simplifies to:
\[ 0 \geq \frac{h}{4\pi} \]
This is mathematically inconsistent because \(\frac{h}{4\pi}\) is a positive constant.

4. **Conclusion about Uncertainty in Momentum**:
Since the equation leads to an inconsistency, it implies that if the uncertainty in position is zero, the uncertainty in momentum (\(\Delta p\)) must be infinite. Therefore:
\[ \Delta p = \infty \]

5. **Select the Correct Answer**:
Among the options provided:
- Zero
- Greater than \( \frac{h}{4\pi} \)
- Less than \( \frac{h}{4\pi} \)
- Infinite

The correct answer is **infinite**.

### Final Answer:
The uncertainty in momentum will be **infinite**.