A particle X of mass m and initial velocity u collides 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 separation after collision   Velocity of approach before collision   =   v y - v x u x - u y ⇒ 1 = v y - v x u - 0 [ ∵   u x = u and u y = 0 ] u = v y - v x       . . . ii From equation (i