The product of uncertainty in velocity and uncertainty in position of a micro particle of mass ' $m$ ' is…
The product of uncertainty in velocity and uncertainty in position of a micro particle of mass ' $m$ ' is not less than in which of the following?
$h \times \frac{3 \pi}{m}$
$\frac{h}{3 \pi} \times m$
$\frac{h}{4 \pi} \times \frac{1}{m}$
$\frac{h}{4 \pi} \times m$
Solution
According to uncertainty principle,
$\begin{aligned}
& \Delta P \cdot \Delta x \geq \frac{h}{4 \pi} \\
& \Rightarrow \quad m . \Delta v \times \Delta x \geq \frac{h}{4 \pi} \\
& \Rightarrow \Delta v \times \Delta x \geq \frac{h}{4 \pi \times m}
\end{aligned}$