Assertion :A particle of mass $M$ at rest decay into two particles of masses $m_{1}$ and $m_{2}$ , having non-zero velocities will have ratio of de-Broglie wavelengths unity. Reason: Here we cannot apply conservation of linear momentum.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
Law of conservation of momentum applies to a system as long as no external forces act on it.
In case of decay, no external force acts on the decaying mass, only internal forces drive the particles away, and hence conservation of linear momentum applies to case of decay. Hence Reason is incorrect.
Since initially the particle was at rest(zero momentum), the momentum of mass $m_{1}$ is equal and opposite to that of $m_{2}$ to give a net zero momentum.
De-broglie wavelength of a particle is $\frac{h}{p}$ , where $p$ is the linear momentum. Since magnitude of momentum of both particles is same, so is the de-Broglie wavelength.

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Assertion :A particle of mass M at rest decay into two particles of masses m1 and m2, having non-zero velocities will have ratio of de-Broglie wavelengths unity. Reason: Here we cannot apply conservation of linear momentum.

Assertion :A particle of mass $M$ at rest decay into two particles of masses $m_{1}$ and $m_{2}$ , having non-zero velocities will have ratio of de-Broglie wavelengths unity. Reason: Here we cannot apply conservation of linear momentum.