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Homework Help: Question about alpha particles

  1. Apr 24, 2010 #1


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    Radium decays emitting alpha particles into Radon.

    i) Explain, in terms of momentum of the particles, why the radon nucleus and the alpha particles move off in opposite directions after the reaction.

    ii) The speed of the radon nucleus after the reaction is [tex] v_{R} [/tex] and that of the alpha particle is [tex] v_{\alpha} [/tex]. Show that the ratio [tex] \frac{v_{\alpha}}{v_{R}} [/tex] is equal to 55.5

    3. The attempt at a solution
    i) To me it is just common sense that Radon and the alpha particle move off in opposite directions because they simply don't want to be together. Radium is trying to get rid of the alpha particle, so when it splits, it's parts just try to go away from each other as much as possible. But I'm not sure whether this answer is correct ?

    ii) The mass of the Radon is about 55.5 times greater than the mass of alpha particle. This means that, if after the reaction the same energy is given to both, the alpha particle and Radon, then alpha particle is going to move 55.5 faster than Radon. The problem is that in my book it is written:
    "Since alpha particle, when ejected, is much smaller than the parent nucleus, it receives almost all of the energy released in the form of Kinetic Energy."

    OK, here it says that indeed, alpha particles have higher energy, but it doesn't say that alpha particles and Radon get the same amount of energy, and since their mass ratio is 55.5, then obviously alpha particle is going to move faster!

    P.S- This is supposed to be a simple question.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 24, 2010 #2
    i) Apply conservation of momentum to find the answer. Consider that at first the Radium nucleus is resting. What do you get?

    Hint: You could also suggest that both nuclei will be moving towards the same direction after the decay, and prove yourself wrong.

    ii) Since the mass of the Radon nucleus is 55,5 times the mass of an alpha particle, try substituting the masses in the above taken conservation of momentum, to get the answer.

    I hope I've helped!
  4. Apr 14, 2012 #3
    No both nuclei wont go in the same direction
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