For a microscopic object `Deltax` is zero than `Deltav` will be ( According to Heisenberg's principle)

Options

A. Zero
B. Inifinite
C. `10^(-23)`
D. `10^(8)`

Answer

To solve the question regarding Heisenberg's Uncertainty Principle, let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding Heisenberg's Uncertainty Principle:**
Heisenberg's Uncertainty Principle states that it is impossible to simultaneously know both the exact position and exact 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,
- \(\Delta p\) is the uncertainty in momentum,
- \(h\) is Planck's constant.

2. **Relating Momentum to Velocity:**
Momentum (\(p\)) is defined as the product of mass (\(m\)) and velocity (\(v\)):
\[ p = m \cdot v \]
Therefore, the uncertainty in momentum can be expressed as:
\[ \Delta p = m \cdot \Delta v \]
where \(\Delta v\) is the uncertainty in velocity.

3. **Substituting into the Uncertainty Principle:**
Substitute \(\Delta p\) into the uncertainty principle equation:
\[ \Delta x \cdot (m \cdot \Delta v) \geq \frac{h}{4\pi} \]

4. **Given Condition:**
According to the problem, \(\Delta x = 0\). Substituting this into the equation gives:
\[ 0 \cdot (m \cdot \Delta v) \geq \frac{h}{4\pi} \]
This simplifies to:
\[ 0 \geq \frac{h}{4\pi} \]
which is not possible.

5. **Analyzing the Implication:**
Since \(\Delta x\) cannot be zero (as it leads to a contradiction), we can rearrange the equation to find \(\Delta v\):
\[ \Delta v \geq \frac{h}{4\pi m \cdot \Delta x} \]
If \(\Delta x = 0\), then the expression becomes:
\[ \Delta v \geq \frac{h}{0} \]
This indicates that \(\Delta v\) approaches infinity.

6. **Conclusion:**
Therefore, if the uncertainty in position (\(\Delta x\)) is zero, the uncertainty in velocity (\(\Delta v\)) will be infinite.

### Final Answer:
If \(\Delta x\) is zero, then \(\Delta v\) will be infinite.

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