Question

A golf ball has a mass of 40g and a speed of 45 m$s^{-1}$. If the speed can be measured with an accuracy of 2%, calculate the uncertainty in the position.

• A. 1.46 $\times$ ${10}^{-33}$ m
• B. 2.62 $\times$ ${10}^{-34}$ m
• C. 7.84 $\times$ ${10}^{-35}$ m
• D. 5.55 $\times$ ${10}^{-33}$ m

Answer 1

The correct option is A

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

By Heisenberg uncertainty principle,

$△p$ $\times$ $△x$ $\ge$ $\frac{h}{4\pi }$ $\Rightarrow$ $△v$ $\times$ $△x$ $\ge$ $\frac{h}{4\pi m}$

Now,

Mass of the ball = 40 g = 40 $\times$ ${10}^{-3}$ kg

The uncertainty in the speed

$△v$ = 45 $\times$ $\frac{2}{100}$ = 0.9 m $s^{-1}$

So the uncertainty in postion,

$△x$ = $\frac{h}{4\pi △p}$ = $\frac{h}{4\pi m△v}$

= $\frac{6.626\times {10}^{-34}}{4\times 3.14\times (40\times {10}^{-3}kg)\times \left(0.9m{s}^{-1}\right)}$

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