Answer:
The final size is nearly the same as the initial size because the increase in size is remarkably small
Solution:
According to the problem:
The proton beam energy is E = 250 GeV =
Distance traveled by the photon, d = 1 km = 1000 m
Proton mass,
Initial size of the wave packet,
Now,
This operates under relativistic principles
The rest mass energy for the proton is expressed as:
This proton energy is
Thus, the speed of the proton, v
The time to cover 1 km = 1000 m of distance is calculated as:
T =
T =
According to the dispersion factor;
Thus, the widening of the wave packet is relatively minor.
Hence, we can conclude that:
where
= final width