Question

Hey guys I could use some help with this problem, tx in advance :)

Problems 7. A very energetic proton detected in the cosmic rays coming to Earth from outer space had a k energy of 1.0 100 ev a. What were its γ and c? b. if the proton traveled across the Milky Way Galaxy, with a diameter of 9.8 10t ly, how long did it take to travel this distance as measured from the reference frame of the Earth? In the reference frame of the proton? c. The de Brogle relationship,papplies relatvisticlly. What is the wavelength of the proton?

Answer 1

a) KE = (Y - 1 ) m c^2

(1 x 10^20 eV x 1.6 x 10^-19 J /eV ) = (Y - 1 ) (1.6726 x 10^-27 x (3 x 10^8)^2)

Y - 1 = 1.06288 x 10^11

Y = 1.06288 x 10^11

Y = 1/ sqrt [1 - (v/c)^2 ] = 1.06288 x 10^11

1 - (v/c)^2 = 8.85175 x 10^-23

v/c is approax 1.

b) t = d / c = 9.8 x 10^4 years

in frame of proton = (9.8 x 10^4 ) / (1.06288 x 10^11)

          = 9.22 x 10^-7 years

time (in sec ) = 9.22 x 10^-7 x ( 365 x 24 x 3600 sec) = 29.08 sec

c) p = Y m v   = 1.06288 x 10^11 x 1.6726 x 10^-27 x 3 x 10^8

         = 5.333 x 10^-8 kg m.s

lambfa = h / p = (6.626 x 10^-34 ) / (5.333 x 10^-8) = 1.242 x 10^-26 m