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% `(Deltav =0.9 km/h)`, what is the uncertainty (in meters) in the position of the car ?

Options

A. ` Delta x ge 1 xx 10 ^( -35 ) m `
B. ` Delta x ge 2 xx 10^( -37 ) ` m
C. ` Delta x ge 2 xx 10 ^( -36 ) m`
D. `Delta x ge 4 xx 10 ^( - 38 ) ` m

Answer

B

Explanation

`Delta x ge (h)/((4pi)(mDeltav))`
`Delta x ge (6.626xx10^(-34))/((4xx3.14xx1050)(00.9)((1)/(3600))((10000)/(1)))`
`Deltax ge 2 xx 10^(-37)m`
The uncertainity in the position of the air is far smaller than the uncertainity in the position of an electron in a hydrogen atom `(3 xx 10^(-10)m)` and far too small a value to have any measurable consequences.