The alpha particle is emitted at 4235 m/s
Explanation:
We can use the law of conservation of momentum to solve the problem: the total momentum of the original nucleus must be equal to the total momentum after the alpha particle has been emitted. Therefore:
 
  
where:  
 is the mass of the original nucleus
 is the mass of the original nucleus
 is the initial velocity of the nucleus
 is the initial velocity of the nucleus
 is the mass of the alpha particle
 is the mass of the alpha particle
 is the final velocity of the alpha particle
 is the final velocity of the alpha particle
 is the mass of the daughter nucleus
 is the mass of the daughter nucleus
 is the final velocity of the nucleus
 is the final velocity of the nucleus
Solving for  , we  find the final velocity of the alpha particle:
, we  find the final velocity of the alpha particle:

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