Dual Nature of Matter

JEE Main level, single correct, medium

40 of 200

Question 40 of 200

A nucleus of mass MM at rest splits into two parts having masses M′3\dfrac{{M}^{'}}{3} and 2M′3(M′<M)\dfrac{2{M}^{'}}{3}\left({M}^{'}\lt M\right). The ratio of de Broglie wavelength of two parts will be

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Answer: (C) 1:11:1

Since the initial momentum of the system is zero. To keep the final momentum zero, the momentum of both parts should be equal and opposite in direction.
∣P⃗1∣=∣P⃗2∣\left|{\vec{P}}_{1}\right|=\left|{\vec{P}}_{2}\right|
Here P⃗\vec{P} is momentum
De-Broglie wavelength is given by λ=hP\lambda =\dfrac{h}{P}
Hence, both will have same de Broglie wavelength.
Therefore, λ1:λ2=1:1{\lambda }_{1}:{\lambda }_{2}=1:1.

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