Question

Electrons are dropped a distance ? down an evacuated tube and strike a target at the bottom. At the top of the tube the electrons’ position is known to some precision determined by the uncertainty principle. Use the uncertainty principle to show that the uncertainty in where the electrons hit the target is given by Δ? = ( 2ℏ ?? ) 1⁄2 ( 2? ? ) 1⁄4 If the tube is 2.0 meters high, what is Δ?.

Answer 1

Here we shall use the position momentum uncertainty principle :