c
(c) By law of conservation of momentum \(0 = {m_1}\overrightarrow {{v_1}} + {m_2}\overrightarrow {{v_2}}\)

\(\Rightarrow {m_1}\overrightarrow {{v_1}} = - {m_2}\overrightarrow {{v_2}} \) -ve sign indicates that both he particles are moving in opposite direction.

Now de-Broglie wavelengths \({\lambda _1} = \frac{h}{{{m_1}{v_1}}}\) and \({\lambda _2} = \frac{h}{{{m_2}{v_2}}}\);

\(\therefore \;\frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{{{m_2}{v_2}}}{{{m_1}{v_1}}} = 1\)