4) The carbon isotope 1\"C is produced in nuclear reactions of cosmic rays in the atmosphere. It is unstable, l\"C. _) 1all + e'+neutrino + 0.156 MeV with a lifetime of 3 2'70 years. a) It is determined that one gram of carbon, newly extracted from the atmosphere, gives on average 15.3 such radioactive decays per minute. What is the proportion of 14(3 isotope in the carbon? b) What count rate would you expect from one gram of carbon extracted from the remains of a wooden hut thought to be 2500 years old, assuming that: the proportion of 1\"\"13 in the atmosphere remains constant and the hut had been built from a fresh timber