Question

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?

• A. $h \times \frac{3 \pi}{m}$
• B. $\frac{h}{3 \pi} \times m$
• C. $\frac{h}{4 \pi} \times \frac{1}{m}$
• D. $\frac{h}{4 \pi} \times m$

Answer 1

Answer: (C)

According to uncertainty principle,

$\Delta p \cdot \Delta x \geq \frac{h}{4 \pi}\,\,\,...(i)$

Here, $\Delta p=$ uncertainty in momentum

$\Delta x=$ uncertainty in position

$h=$ Planck's constant

Since, $p=m v$

Hence,

$\Delta p=m \Delta v$

Putting the value of $\Delta p$ in the expression

$m \cdot \Delta v \times \Delta x \geq \frac{h}{4 \pi} $

$\Delta v \times \Delta x \geq \frac{h}{4 \pi \times m}$