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A particle \( A \) of mass \( m \) and initial velocity \( v \) 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
[JEE (Main) 2017]
(a) \( \frac{\lambda_{A}}{\lambda_{B}}=\frac{1}{2} \)
(b) \( \frac{\lambda_{A}}{\lambda_{B}}=\frac{1}{3} \)
(c) \( \frac{\lambda_{A}}{\lambda_{B}}=2 \)
(d) \( \frac{\lambda_{A}}{\lambda_{B}}=\frac{2}{3} \)
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