Question

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

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

$\Delta x \ge \frac{6.626\times10^{-34}}{\left(4\times3.14\times1050\right)\left(0.9\right)\left(\frac{1}{3600} \right)\left(\frac{1000}{1}\right)}$

$\Delta x \ge 2\times10^{-37 }\,m$

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.