It is not possible to determine precisely both the position and momentum (or velocity) of a small moving particle such as electron, proton etc. This is known as Heisenberg uncertainty principle. The mathematical form of this principle is :
`Delta x.Delta p ge (h)/(4pi)` (constant)
However this principle is irrelevant in case of bigger particles such as a cup, ball, car etc., that we come across in our daily life.
If the uncertainty in position of the electron is zero, the uncertainty in its momentum would be

Options

A. zero
B. greater than `h//4pi`
C. less than `h//4pi`
D. infinite.

Explanation

To solve the problem regarding the Heisenberg uncertainty principle, we will follow these steps:

### Step 1: Understand the Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle states that it is impossible to simultaneously know both the exact position (Δx) and the exact momentum (Δp) of a particle. The mathematical expression for this principle is given by:

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

where \( h \) is Planck's constant.

### Step 2: Identify the Given Information
In this problem, we are told that the uncertainty in the position of the electron (Δx) is zero:

\[ \Delta x = 0 \]

### Step 3: Substitute the Value into the Uncertainty Principle
We need to find the uncertainty in momentum (Δp). According to the uncertainty principle, we can rearrange the formula to solve for Δp:

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

### Step 4: Substitute Δx into the Equation
Now, substituting Δx = 0 into the equation:

\[ \Delta p \geq \frac{h}{4\pi \cdot 0} \]

### Step 5: Analyze the Result
Since division by zero is undefined in mathematics, this implies that:

\[ \Delta p \geq \infty \]

This means that if the uncertainty in position is zero, the uncertainty in momentum becomes infinitely large.

### Conclusion
Thus, the uncertainty in momentum (Δp) would be infinite.

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

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