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Uranium (Mass number 238) originally at rest, decays by emitting an alpha particle having a speed u. What is the recoil speed of the residual nucleus in terms of u ?

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Uranium (Mass number 238) originally at rest, decays by emitting an alpha particle having a speed u. What is the recoil speed of the residual nucleus in terms of u ?

Alpha mass = 4

Residual nucleus = Thorium – 234

Conservation of momentum Since the U-238 nucleus is at rest, the initial momentum is 0.

Final momentum = 4 * u + 234 * v

4 * u + 234 * v = 0

v = -4/234 * u

The negative sign means the Thorium nucleus is traveling in the opposite direction of the alpha particle.