A nucleus of mass M + m is at rest and decays into two daughter nuclei of equal mass M/2 each. The speed of daughter nuclei is: - Physics MCQ AIEEE 2026 | ExamTest.live | ExamTest.live

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A nucleus of mass M + Δ m is at rest and decays into two daughter nuclei of equal mass M /2 each. The speed of daughter nuclei is:

A $c \frac{Δ m}{M + Δ m}$
B $c \frac{2Δ m}{M}$
C $c \frac{Δ m}{M}$
D $c \frac{2Δ m}{M + Δ m}$

Solution & Step-by-step Explanation

By conservation of energy:Initial energy = Final energy (M + Δ m) c^{2} = 2 \times [rest mass energy of daughter + K.E. of daughter] (M + Δ m) c^{2} = 2 \times [\frac{M}{2} c^{2} + \frac{1}{2} (\frac{M}{2}) v^{2}] (M + Δ m) c^{2} = M c^{2} + \frac{M}{2} v^{2} Δ m c^{2} = \frac{M}{2} v^{2} v^{2} = \frac{2Δ m c ^{2}}{M} v = c \frac{2Δ m}{M}

Practice this question

Try it yourself before checking the explanation above.

A nucleus of mass M + Δ m is at rest and decays into two daughter nuclei of equal mass M /2 each. The speed of daughter nuclei is:

A

c \frac{Δ m}{M + Δ m}

B

c \frac{2Δ m}{M}

C

c \frac{Δ m}{M}

D

c \frac{2Δ m}{M + Δ m}

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Nuclear Physics Mass-Energy Equivalence

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