Question

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

• A. $2.52\times {10}^{-33}m$
• B. $3.02\times {10}^{-33}m$
• C. $1.46\times {10}^{-33}m$
• D. $0.82\times {10}^{-33}m$

Answer 1

Answer: (C)

Use Heisenberg's uncertainty principle.

For example $[\Delta x=\frac{h}{4\pi m\Delta v}]$

Here, $\Delta x$ is the uncertainty in the position.

$\Delta v$ is the uncertainty in velocity

m is the mass of Particle.

Given,$m=40g=0.04kg$

$\Delta v=2\%ofv=2\times \frac{45}{100}=0.9m/s$

$h=6.626\times {10}^{-34}J.s$

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

$=1.4654\times {10}^{-33}m$

So, the correct option is $C$