Answer :

Mass of the uranium-238 nucleus, m = 238

Initial speed of the nucleus, u = 0 m/s


Final speed of the nucleus = v


Final speed of the alpha particle, v2 = 1.4 × 107 m/s


Mass of the nucleus after emission, m1 = 234


Mass of the alpha particle, m2 = 4


Applying conservation of momentum, mu = m1v1 + m2v2


238×0 = 234×v + 4×1.4×107


234v = –5.6×107


v = –2.39×105 m/s ≈ –2.4×105 m/s


Recoil speed of nucleus is 2.4×107 m/s opposite to the direction of emission of alpha particle.


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