Ahypothetical particle x has a measured mass of 600 mev/c2, decaying with a lifetime τ of 10-20 sec. two-thirds of the time it decays to mode 1, one-third of the time it decays to mode 2. a. what are the partial decay rates, expressed in s-1 to modes 1 and 2? b. suppose we have 10 x particles at time t=0. at time t=5x10-20 sec, what is the average number of x particles that remain? what is the most likely number of x particles that remain? c. how far would the x particle travel, on average, if it had a momentum of 800 mev/c?