Solve the below:
Uncertainty Principle Beam of Electrons
Section 1
A beam of electrons traveling with speed 7 × 10 ^7 m/s passes through a slit of width 1 × 10 ^(-5) m. Because of the uncertainty in the lateral position of the beam, there will be an uncertainty in the transverse momentum as well.
Estimate this uncertainty, and use it to calculate the spread of the image of the electron beam on a photographic plate placed perpendicular to the beam at a distance of 2 m beyond the slit.
Section 2
The rest-energy of the Z 0 boson is 77 GeV. Find the maximum length of time a virtual Z 0 can exist in accordance with the uncertainty principle.