Question

The uncertainty in the position of an electron moving with velocity of $3 \times 10^{4} cm / s$ is (given mass of electron $=9.1 \times 10^{-28}$, uncertainty in velocity $=0.02 \%$ )

• A. $1.8 \times 10^{-3} cm$
• B. $9 \times 10^{-3} cm$
• C. $3.8 \times 10^{-2} cm$
• D. $1.8 \times 10^{-4} cm$

Answer 1

Answer: (B)

Heisenberg's uncertainty equation,
$\Delta x \times \Delta P \geq \frac{h}{4 \pi}$
$\Rightarrow \Delta x \times m \Delta v \geq \frac{h}{4 \pi}$
$\therefore \Delta x=$ uncertainty in position
$\Delta P=m \Delta v=$ uncertainty in momentum
$\Rightarrow \Delta x=\frac{h}{4 \pi \times m \times \Delta v}$
$=\frac{6.626 \times 10^{-27} \text { ergs }}{4 \times 3.14 \times\left(9.1 \times 10^{-28} g\right)} \times\left(3 \times 10^{4} \times \frac{0.02}{100} cms ^{-1}\right)$
$=9.66 \times 10^{-3} cm$
So, in option (b) answer should be written as
$9.66 \times 10^{-3} cm$ or $9 \times 10^{-3} cm$.