Question

The uncertainty in the velocity of particle of mass $6.626 \times 10^{-28} Kg$ is $10^{-6} m / sec .$ What is the uncertainty in its position in $nm ?$

• A. $1 / 2 \pi$
• B. $2.5 / \pi$
• C. $4 / \pi$
• D. $1 / 4 \pi$

Answer 1

Answer: (D)

According to Heisenberg's uncertainty principle

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

$m =6.626 \times 10^{-28} kg$

$\Delta v =10^{-6} m / sec$

$h =6.626 \times 10^{-34} Js$

$6.626 \times 10^{-28} \times 10^{-6} \times \Delta x =\frac{6.626 \times 10^{-34}}{4 \pi}$

$\Delta x=\frac{6.626 \times 10^{-34}}{4 \pi \times 6.626 \times 10^{-34}}=\frac{1}{4 \pi}$