If uncertainity in position is zero, the uncertainity in momentum of an electron will be

Options

A. Zero
B. Infinity
C. Unity
D. Zero or infinity

Answer

To solve the question, we will use Heisenberg's Uncertainty Principle, which relates the uncertainties in position and momentum of a particle.

### Step-by-Step Solution:

1. **Understanding Heisenberg's Uncertainty Principle**:
The principle states that the product of the uncertainties in position (Δx) and momentum (Δp) of a particle is always greater than or equal to a constant value. Mathematically, it is expressed as:
\[ Δx \cdot Δp \geq \frac{h}{4\pi} \]
where \(h\) is Planck's constant.

2. **Given Information**:
In the question, we are given that the uncertainty in position (Δx) is zero:
\[ Δx = 0 \]

3. **Substituting into the Uncertainty Principle**:
We can substitute Δx into the uncertainty principle equation:
\[ 0 \cdot Δp \geq \frac{h}{4\pi} \]
This simplifies to:
\[ 0 \geq \frac{h}{4\pi} \]
This inequality cannot hold true since \(\frac{h}{4\pi}\) is a positive value.

4. **Analyzing the Implication**:
Since Δx is zero, we can rearrange the original equation to find Δp:
\[ Δp \geq \frac{h}{4\pi Δx} \]
Substituting Δx = 0 into this equation gives:
\[ Δp \geq \frac{h}{4\pi \cdot 0} \]
This results in:
\[ Δp \geq \text{infinity} \]
Therefore, the uncertainty in momentum (Δp) tends to infinity.

5. **Conclusion**:
Thus, if the uncertainty in position is zero, the uncertainty in momentum of an electron will be infinite.

### Final Answer:
The uncertainty in momentum (Δp) will be infinite.

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