Electron Interference and Star Trek

A situation where matter waves could become important is the Star Trek transporter. We are not sure how a transporter would really work, but for the purposes of this activity, let us suppose that it decomposes a person into his or her component atoms. Then, it sends the atoms to a new location where the person is reconstructed.

Consider transporting Captain Janeway of the Voyager by such a method. She wishes to reach her new location quickly, so her atoms are sent out of the ship at 10% of the speed of light (3 x 10⁷ m/s). Assume that her atoms have a mass of 10^-26 kg.

What is the de Broglie wavelength of each matter wave?

Each atom must be transmitted through the titanium hull of the starship. The titanium can be considered as a large number of slits separated by 1 nm.

Must the designers of the transporter be concerned about diffraction effects as the captain’s atoms are beamed through the hull of the Enterprise? Why or why not?

Would this effect make a good premise for a Star Trek movie? Why or why not?