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Two particles, each having the same de Broglie wavelength lambda, collide and merge to form a single new particle. The new particle also has de Broglie wavelength lambda. What must be the angle between the initial directions of motion of the two particles?

1. 60 deg
2. 30 deg
3. 120 deg
4. None of these

Correct answer: 120 deg

Solution

Conservation of momentum: |p_total|² = p1² + p2² + 2p1*p2*cos(theta) = p² + p² + 2p²*cos(theta). For the resultant momentum magnitude to be p (wavelength = lambda), we need p² = 2p²(1 + cos(theta)), giving cos(theta) = -1/2, so theta = 120 deg.

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