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