A particle X of mass m and initial velocity u collide with another particle Y of mass 3 m 4 which is at rest, The collision is head on and perfectly elastic. The ratio of de-Broglie wavelengths λ Y and λ X after the collision is

Step-by-step solution

For perfectly elastic collision, total momentum before collision = total momentum after collision i.e. m · u + 3 m 4 × 0 = m v x + 3 m 4 · v y ⇒ 4 u = 4 v x + 3 v y       . . . i Coefficient of restitution, e = Velocity   of   seperation   v y - v x   after   collision   Velocity   of   approach u x - u y   before   collision   ⇒ 1 = v y - v x u - 0 [ ∵   u x = v and u y = 0 ] u = v y - v x     &#16