Question

The uncertainty in the momentum of an electron is ${10}^{-6}kgm{s}^{-1}$. What will be the uncertainty in its position? [$h=6.6\times -{10}^{-34}Js$]

• A. $1.65\times {10}^{-28}$m
• B. $1.65\times {10}^{-40}$m
• C. $5.25\times {10}^{-29}$m
• D. $5.25\times {10}^{-40}$m

Answer 1

The correct option is C $5.25\times {10}^{-29}$m

Uncertainty in the momentum $={10}^{-6}$kgm$s^{-1}$

$\Delta P={10}^{-6}$ kgm$s^{-1}$

$\Delta P\cdot \Delta x\ge \frac{b}{4z}$

$\Delta x\ge \frac{h}{4z\Delta p}$

$\Delta x\ge \frac{6.626\times {10}^{-34}}{4\times 3.14\times {10}^{-6}}$

$\Delta x\ge 5.27\times {10}^{-29}m$

Option C.