Question

The uncertainty in the momentum of an eklectron is $10\times {10}^{-5}kgm{s}^{-1}$.The uncertainty in its position will be:

$(h=6.62\times {10}^{-34}kg{m}^2{s}^{-1})$

• A. $1.05\times {10}^{-28}$
• B. $1.05\times {10}^{-26}$
• C. $5.27\times {10}^{-31}$
• D. $5.25\times {10}^{-28}$

Answer 1

Answer: (C)

$5.27\times {10}^{-31}$

Uncertainty in momentum $\Delta P=10\times {10}^{-5}kgm{s}^{-1}$

According to Heisenberg uncertainty principle

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

$10\times {10}^{-5}\Delta x\ge \frac{6.626\times {10}^{-34}}{4\times 3.14}$

$\Delta x\ge \frac{6.626\times {10}^{-34}}{4\times 3.14\times 10\times {10}^{-5}}$

$\Delta x\ge 0.5275\times {10}^{-30}$

$\Delta x\ge 5.275\times {10}^{-31}$.