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A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelength of A to B after the collision is -

1. λA/λB = 1/3
2. λA/λB = 2
3. λA/λB = 2/3
4. λA/λB = 1/2

Correct answer: λA/λB = 2

Solution

In an elastic collision, momentum and kinetic energy are conserved. After the collision, particle A, having a mass m, moves with a reduced velocity, while particle B, with mass m/2, gains velocity. The de-Broglie wavelength is inversely proportional to momentum, and since particle B has a greater velocity after the collision, its wavelength becomes shorter, leading to the ratio of the wavelengths being 2.

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