A particle A of mass m and initial velocity v collides with a particle B of mass m 2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λ A to λ B after the collision is:

Step-by-step solution

m V = m V A + m 2 V B V = V A + V B 2 − − − − − − − − − − − − (i) V = V B − V A − − − − − − − − − − − − (ii) Solving (i) and (ii) 2 V = 3 V B 2 ∴ V B = 4 V 3 V A = V B − V = V 3 P A = m V 3 P B = m 2 . 4 V 3 λ A λ B = h × P B P A × h = 2 m V 3 m V 3 = 2