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Two particles move at right angles to each other. Their de-Broglie wavelengths are ${"mathml":"<math class="image_resized" style="width:15px;height:16px"><span style="font-family:$ and ${"mathml":"<math class="image_resized" style="width:15px;height:16px"><span style="font-family:$ respectively. The particles are undergoing perfectly inelastic collisions. The de-Broglie wavelength ${"mathml":"<math class="image_resized" style="width:8px;height:11px"><span style="font-family:$ , of the final particle, is found to have.

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${"mathml":"<math class="image_resized" style="width:118px;height:44px"><span style="font-family:$

answer is D.(Unlock A.I Detailed Solution for FREE)

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Detailed Solution

Concept- Determine the momentum of both particles first. then include momentum conservation into it. We shall obtain a vector of total momentum. It is important to ascertain the outcome.

P → 1 = h A^λ 1

and P → 2 = h A^λ 2

Using momentum conservation

P → = P → 1 + P → 2

= h λ 1 λ 1 + h A j λ 2

| P → | = h λ 1 2 + h λ 2 2

h λ = h λ 1 2 + h λ 2 2

1 λ 2 = 1 λ 12 + 1 λ 22

Hence, option 4 is correct.

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