Question

Determine uncertainty in the position of an electron moving with a velocity 300 m. sec${}^{-1}$ accurate up to 0.001 %

[ $h=6.63\times {10}^{-34}$ J.s and mass of electron $=9.1\times {10}^{-31}$ kg]

• A. $1.92\times {10}^{-2}$ m
• B. $1.5\times {10}^{-2}m$
• C. $2.5\times {10}^{-2}m$
• D. $2.5\times {10}^{-3}m$

Answer 1

The correct option is A $1.92\times {10}^{-2}$ m

The uncertainty in position ($\Delta x$) can be calculated as follows:

$\Delta x=\frac{h}{4\pi }\frac{1}{m\Delta v}$.

$\Delta x=\frac{6.63\times {10}^{-34}Js}{4\times 3.14\times 9.1\times {10}^{-31}kg\times 3\times {10}^{-3}m{s}^{-1}}$

$\Delta x=1.93\times {10}^{-2}m$

Hence, the correct option is $A$.