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Question

Physics Question on Nuclei

A nucleus of mass M+ΔmM + \Delta m is at rest and decays into two daughter nuclei of equal mass M2\frac{M}{2} each. Speed of light is cc The speed of daughter nuclei is

A

cΔmM+Δmc \frac{\Delta m}{M+\Delta m}

B

c2ΔmMc \sqrt{\frac{2\Delta m}{M}}

C

cΔmMc \sqrt{\frac{\Delta m}{M}}

D

cΔmM+Δmc \sqrt{\frac{\Delta m}{M+\Delta m}}

Answer

c2ΔmMc \sqrt{\frac{2\Delta m}{M}}

Explanation

Solution

Conserving the momentum 0=M2V1−M2V20 = \frac{M}{2} V_{1} -\frac{M}{2} V_{2} V1=V2…………… .(1)V_{1} = V_{2} \quad\dots\dots\dots\dots\dots.\left(1\right) Δmc2=12.M2V12+12.M2.V22…………… .(2)\Delta mc^{2} = \frac{1}{2}. \frac{M}{2} V_{1}^{2} + \frac{1}{2}.\frac{M}{2} .V_{2}^{2}\quad\dots\dots\dots\dots\dots.\left(2\right) Δmc2=M2V12\Delta mc^{2} = \frac{M}{2} V_{1}^{2} 2Δmc2M=V12\frac{2\Delta mc^{2}}{M} = V^{2}_{1} V1=c2ΔmMV_{1} = c \sqrt{\frac{2\Delta m}{M}}