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Answer:
The final size is approximately equal to the initial size due to a very small relative increase of in its size
Solution:
As per the question:
The energy of the proton beam, E = 250 GeV =
Distance covered by photon, d = 1 km = 1000 m
Mass of proton,
The initial size of the wave packet,
Now,
This is relativistic in nature
The rest mass energy associated with the proton is given by:
This energy of proton is
Thus the speed of the proton, v
Now, the time taken to cover 1 km = 1000 m of the distance:
T =
T =
Now, in accordance to the dispersion factor;
Thus the increase in wave packet's width is relatively quite small.
Hence, we can say that:
where
= final width