Question

Table-tennis ball has a mass 10 g and a speed of 100m/s. If speed can be measured within an accuracy of 10%, what will be the uncertainty in speed and position respectively?

• A. $10,4\times {10}^{-33}$
• B. $10,5.27\times {10}^{-34}$
• C. $0.1,5\times {10}^{-34}$
• D. None of these

Answer 1

Answer: (B)

$10,5.27\times {10}^{-34}$

According to Heisenberg's uncertainity principle:

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

$\Delta x.\Delta \left(mv\right)=\frac{h}{4\pi }$

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

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

$m=$mass of ball$=10g={10}^{-2}$ kg

speed of ball, v=100 m/s and accuracy of measurement = 10%

Uncertainity in speed:

$\therefore \Delta v=\frac{10}{100}\times v=\pm 10$ m/s

upon substitution we get:

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

$\Delta x=5.27\times {10}^{-34}$ m

Thus the uncertainty in speed and position is $10m/s$ and $5.27\times {10}^{-34}m$ respectively