Question

A golf ball has a mass of $40$ g, and a speed of $45$ m/s, if speed can be measured within accuracy of $2\%$, calculate the uncertainty in the position.

• A. $1.56\times {10}^{-30}$
• B. $1.46\times {10}^{-33}$ m
• C. $1.47\times {10}^{-23}$ m
• D. $1.47\times {10}^{-30}$ m

Answer 1

Answer: (B)

$1.46\times {10}^{-33}$ m

Using heisenberg's uncertainty principle,

$\Delta =h/4\pi m\Delta v$

$\Delta x$ = uncertainty in position

$\Delta v$$=2$$\times$$45/100=0.9$ m/s

now $\Delta x=\frac{6.626\times {10}^{-34}}{(4\times 3.14\times 0.04\times 0.9)}$

$=1.46\times {10}^{-33}$ m