Question

What will be the uncertainty in velocity of a bullet with a mass of 10 g whose position is known with $\pm 0.01mm$?

• A. $5.275\times {10}^{-33}m{s}^{-1}$
• B. $5.275\times {10}^{-25}m{s}^{-1}$
• C. $5.275\times {10}^{-5}m{s}^{-1}$
• D. $5.275\times {10}^{-28}m{s}^{-1}$

Answer 1

Answer: (D)

$5.275\times {10}^{-28}m{s}^{-1}$

According to Heisenberg's uncertainity principle:

$\Delta x.\Delta p=\frac{h}{4\pi }$

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

Given: $h=6.626\times {10}^{-34}Js$=Planck's constant

$m=$mass of object $=10g=0.01$ kg and $\Delta x=\pm 0.01mm=\pm 0.01\times {10}^{-3}m={10}^{-5}m$

Upon substitution we get:

$\Delta v=\frac{6.626\times {10}^{-34}}{{10}^{-5}\times 4\times 3.14\times {10}^{-2}}$

$\Delta v=0.527\times {10}^{-27}=5.27\times {10}^{-28}$ m/s