QJEEM19Ph92be: JEE Main 2019 Physics - Class 12 JEEM19Ph92be Solution: Two particles move at right angle to each other. Their…

Question

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Two particles move at right angle to each other. Their de-Broglie wavelengths are

λ_{1}

and

λ_{2}

respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength

λ_{2}

of the final particle, is given by :

Accepted Answer

Let the two particles be moving along x-direction and y-direction.

So, the net momentum initially is

\sqrt{\frac{h^{2}}{λ_{1}^{2}} + \frac{h^{2}}{λ_{2}^{2}}}

and final momentum will be

\frac{h}{λ}

.

Applying momentum conservation,

\frac{h}{λ} = \sqrt{\frac{h^{2}}{λ_{1}^{2}} + \frac{h^{2}}{λ_{2}^{2}}}

\Rightarrow

\frac{1}{λ^{2}} = \frac{1}{λ_{1}^{2}} + \frac{1}{λ_{2}^{2}}

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