15 A deuteron mass 2u where u is the atomic mass uni is trav

15. A deuteron (mass 2u, where u is the atomic mass uni) is traveling at speed to and collides elastically with a neutron (mass lu) initially at rest. After the collision, the two particles are moving in the same direction (i.e., this is a one-dimensional collision). The final speed of the neutron is A) 2vo B) (4/3)o C) vo D) (3/2)o E) (2/3)o

Solution

Mass of deuteron m = 2u

Initial velocity of deuteron u = vo

Mass of neutron M = 1u

Initial velocity of neutron U = 0     Since it is at rest

Let the final speed of neutron be V and final speed of deuteron be v

For elastic collison , coefficient of restituion e = 1

i.e., relative velocity after collision / relative velocity before collision= 1

    ( V - v ) /( u -U ) = 1

                  V - v = u - U

                         = vo - 0

                         = vo

                      v = V -vo

From law of conservation of momentum ,

mu + MU = mv + MV

(2u)vo +(1u)0 = (2u)(V-vo) +(1u) V

             2vo = 2(V-vo)+V

                   = 2V -2vo +V

                   = 3V -2vo

              3V = 4vo

                V =(4/3)vo