Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $${{\lambda _1}}$$/$${{\lambda _2}}$$, is given by:

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 $${\lambda _A}$$ to $${\lambda _B}$$ after the collision is: