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Two identical particles are moving in opposite directions and are associated with de Broglie wavelengths of $λ_{1}$ and $λ_{2} (λ_{1} < λ_{2}) .$ . If they collide and the collision is completely inelastic, then the de Broglie wavelength of the compound particle is

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$\frac{2 λ_{1} λ_{2}}{λ_{2} - λ_{1}}$

$\sqrt{λ_{1} λ_{2}}$

$\frac{λ_{1} λ_{2}}{λ_{2} - λ_{1}}$

$\frac{λ_{1} + λ_{2}}{2}$

answer is C.

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Detailed Solution

$λ_{1} = h / p_{1} and λ_{2} = h / p_{2} .$ The magnitude of total momentum after collision is $p_{1} - p_{2} \cdot λ = \frac{h}{(p_{1} - p_{2})}$

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