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, we can follow these steps:

### Step 1: Understand Heisenberg's Uncertainty Principle
Heisenberg's Uncertainty 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, this is expressed as:
\[ Δx \cdot Δp \geq \frac{h}{4\pi} \]
where \( h \) is Planck's constant.

### Step 2: Relate momentum to velocity
Momentum (p) can be expressed in terms of mass (m) and velocity (v):
\[ p = m \cdot v \]
Thus, the uncertainty in momentum can be expressed as:
\[ Δp = m \cdot Δv \]
where \( Δv \) is the uncertainty in velocity.

### Step 3: Substitute into the uncertainty principle
Substituting the expression for momentum into the uncertainty principle gives:
\[ Δx \cdot (m \cdot Δv) \geq \frac{h}{4\pi} \]

### Step 4: Analyze the case when Δx = 0
If we consider the case where the uncertainty in position (Δx) is zero:
\[ 0 \cdot (m \cdot Δv) \geq \frac{h}{4\pi} \]
This leads to:
\[ 0 \geq \frac{h}{4\pi} \]
This is not possible, as \( \frac{h}{4\pi} \) is a positive constant.

### Step 5: Conclude about Δv
To satisfy the inequality, if Δx is zero, then Δv must approach infinity. This means that if we have no uncertainty in position, the uncertainty in velocity becomes infinitely large.

### Final Answer
Thus, according to Heisenberg's principle, if Δx is zero, then Δv will be infinite.