Atoms & Nuclei

JEE Main level, single correct, medium

222 of 239

Question 222 of 239

In a nuclear fission reaction of an isotope of mass MM, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect ΔM\Delta M will be :

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Answer: (C) c2ΔMMc\sqrt{\dfrac{2\Delta M}{M}}

Let the reaction be, (P)→(X)+(Y)+(Z)(P)\rightarrow (X)+(Y)+(Z)
Let mass of each daughter nuclei be mm, then mass defect can be written as ∆M=M−3m∆M=M-3m.
Now the energy released will be in the form of kinetic energy of the daughter nuclei. Therefore,
ΔMc2=12mV2+12mV2+12mV2⇒V=2ΔMc23m=2ΔMc2M−∆M≈c2ΔMM\Delta M{c}^{2}=\dfrac{1}{2}m{V}^{2}+\dfrac{1}{2}m{V}^{2}+\dfrac{1}{2}m{V}^{2} \Rightarrow V=\sqrt{\dfrac{2\Delta M{c}^{2}}{3m}}=\sqrt{\dfrac{2\Delta M{c}^{2}}{M-∆M}}\approx c\sqrt{\dfrac{2\Delta M}{M}}

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