A particle A of mass m and initial velocity v m collides with a particle B of mass \[\frac{m}{2}\] which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths \[{{\lambda }_{A}}\] to \[{{\lambda }_{B}}\] after the collision is

• A. \[\frac{2}{3}\]
• B. \[\frac{1}{2}\]
• C. \[\frac{1}{3}\]
• D. \[2\]