Question

Assume that you are travelling at a speed of $90km/h$ in a small car with a mass of $1050kg$. If the uncertainty in the velocity of the car is $1\%$ $(\Delta v=0.9km/h)$, what is the uncertainty (in meters) in the position of the car ?

• A. $\Delta x\ge 1\times 10^{-35}$ m
• B. $\Delta x\ge 2\times 10^{-37}$ m
• C. $\Delta x\ge 2\times 10^{-36}$ m
• D. $\Delta x\ge 4\times 10^{-38}$ m

Answer 1

Answer: (B)

$\Delta x\ge \frac{h}{\left(4\pi \right)\left(m\Delta v\right)}$

$\Delta x\ge \frac{6.626\times 10^{-34}}{\left(4\times 3.14\times 1050\right)\left(0.9\right)\left(\frac{1}{3600}\right)\left(\frac{1000}{1}\right)}$

$\Delta x\ge 2\times 10^{-37}m$

The uncertainty in the position of the car is far smaller than the uncertainty in the position of an electron in a hydrogen atom $(3\times 10^{-10}m)$ and far too small a value to have any measurable consequences.