Answer:
a) Approximately 0.2066 m
b) 0.00002568443 s
c) Approximately 188.87 s
Step-by-step explanation:
a) The total energy of the electron = 190GeV
The rest energy of the electron = 0.51 MeV



u = √(299792458² × (1 - 1/37254.902²)) = 299792457.892
β = v/c = 299792457.892/299792458 = 0.99999999964

Δx = √(Δx'²×(1 - β²)) = √(7700²×(1 - 0.99999999964²)) ≈ 0.2066 m
The length of the tube in the electron's frame ≈ 0.2066 m
b) The time in the frame of the electron is given as follows;
Δt' = 7700/299792457.892 = 0.00002568443 s
c) The time in the frame of the tube is given as follows;

1 - β² = (Δt'/Δt)²
Δt = √(Δt'/(1 - β²)) = √(0.00002568443 /(1 - 0.99999999964²)) ≈ 188.87 s.