# Uncertainty

QUESTION:
The speed of bullet with a mass = 0.050 kg and speed = 420 m/s. Uncertainty = 0.010%..
What is the minimum uncertainty in the bullet's position if is measured at the same time as
the speed is measured?

Choices to pick from:

(a) 2.5 x 10

^{-31} m

(b) 5.0 x 10

^{-32} m

(c) 7.5 x 10

^{-33} m

(d) 2.5 x 10

^{-34} m

(e) 6.0 x 10

^{-36} m

## Answer

The uncertainty in momentum is 0.01% of 0.05x420 = 21x0.01/100 =
0.0021

The uncertainty in position = Planck's constant/[2

p x Uncertainty in momentum]

=
6.63x10

^{-34}/[6.28 x0.0021] = 5.02x10

^{–32} m

The answer is
(b).