Neutrons have a proper half-life of 610 seconds. it has been theorized that extremely energetic neutrons could be produced by collisions of ultra-energetic protons (accelerated by an unknown mechanism) with nuclei. for a collection of neutrons to reach earth with 50% surviving, what is c – v in m/s if they are created near a star cluster 10,000 light-years distant? hint: you can express βγ in terms of an extremely large quantity, solve for β and apply the binomial approximation to simplify the solution. (see one of us if you get stuck.)