Assertion (A): A particle of mass M at rest d | vedclass

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(C) According to the law of conservation of linear momentum,since the initial particle of mass $M$ is at rest,the total initial momentum is $0$.Theref

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If Assertion is true but Reason is false.

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(C) According to the law of conservation of linear momentum,since the initial particle of mass $M$ is at rest,the total initial momentum is $0$.Therefore,the two resulting particles must have equal and opposite momenta: $|p_1| = |p_2| = p$.The de-Broglie wavelength is given by $\lambda = \frac{h}{p}$.Since both particles have the same magnitude of momentum $p$,their de-Broglie wavelengths are $\lambda_1 = \frac{h}{p}$ and $\lambda_2 = \frac{h}{p}$.Thus,the ratio $\frac{\lambda_1}{\lambda_2} = 1$,which means the ratio is unity. So,the Assertion $(A)$ is true.However,the Reason $(R)$ states that we cannot apply the conservation of linear momentum,which is false because the conservation of linear momentum is always applicable in the absence of external forces. Thus,the Reason is false.

Assertion $(A):$ $A$ particle of mass $M$ at rest decays into two particles of masses $m_1$ and $m_2$,having non-zero velocities. The ratio of their de-Broglie wavelengths is unity.
Reason $(R):$ Here,we cannot apply the conservation of linear momentum.

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Assertion $(A):$ $A$ particle of mass $M$ at rest decays into two particles of masses $m_1$ and $m_2$,having non-zero velocities. The ratio of their de-Broglie wavelengths is unity.Reason $(R):$ Here,we cannot apply the conservation of linear momentum.