Question

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Question 4 our atmosphere, making extensive showers of secondary particles that can be measured in detectors which observe the ionization they create as they descend through our atmosphere. Most cosmic rays are protons photons. But a few years ago a puzzling phenomenon was observed: type" appeared to be coming from a bizarre deep space object known as Cygnus X3. The reason this was puzzling fields. They should not appear to "point back to" their source. Scientists looked around for other particles that satisfied three conditions: Cosmic Ray Neutrons. Cosmic rays are particles from interstellar space that impact on some cosmic rays of the "proton or was that protons travel on helical paths on their way to Earth in response to interstellar magnetic They had to be stongly interacting, so they could make proton type showers. They had to be electrically neutral, so they would not be bent by interstellar magnetic fields. They would have to live long enough to make it from their source to Earth One obvious candidate is the neutron. It has an average lifetime of 885.7t 0.8 sec a) Assuming the distance to Cygnus X3 is 10,000 light-years, what is the minimum speed that a neutron must be traveling so that it could make it to Earth in its own proper lifetime? b) Assume that the distance to Cygnus X3 was not well known at the time. The experimenters could estimate the y factor of the cosmic rays as they entered the laboratory. They found that y1010. Approx- imately how far away could Cygnus X3 be if neutrons are the source of the puzzling cosmic rays? These results were deemed unrealistic, and the neutron was discarded as a possible source of these rays.

Answer 1

Given: Lifetime of neutrino (to) = 885.7 sec (with 0.8 sec uncertainty) (a) Cygnus X3 distance (d) = 104 light year =10*xcx 3.15 x 10 m (3.15x10':number of sec in a year) Velocity of neutrino to make it to the earth (v) = ? If the life time of neutrino in its own frame is t, which in turn would be =d/v, So, t= t./[(1-(v2/c)]1/2 = d/v => d? (1-(v2/c)] = v2t2. (squaring both side and rearranging) => v2 = c/[(ct./ d)2 +1] (Collecting v2 term and rearranging) =>v = c[(ct./ d)2 +1]1/2 (Collecting v2 term and rearranging) = c [lct./ 104 xcx 3.15 x 107)2 +1)-1/2 = c [(8.86x10²/104 x 3.15 x 107)2 +1]-1/2 (cancelling c from numerator and denominator) = c [( 2.8x109)2 +1)-1/2 = C (1+ 7.9x 10-187-1/2 C[1-3.95x 10-18 +other higher order terms] (Bionomial Expansion of-1/2 power) VC (b) y = 1010 d=? t=yt. = d/v => d = vyt. zeyt. cyt. /cx 3.15x107 light year -8.86x102 x 1010/3.15x107 light year 2.81 x 105 light year