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    How can you manipulate the two equations to get the 3rd equation for kinetic energy of an alpha particle (in alpha decay).

    d: daughter nucleus




    It seems like it's just a matter of some simple algebra but I'm having a complete brain fade atm.

    Any help would be much appreciated. Thanks
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    (Original post by Marc Fiorano)
    How can you manipulate the two equations to get the 3rd equation for kinetic energy of an alpha particle (in alpha decay).

    d: daughter nucleus




    It seems like it's just a matter of some simple algebra but I'm having a complete brain fade atm.

    Any help would be much appreciated. Thanks
    It is simple algebra. Assume the nucleus is stationary when it decays, i.e. linear momentum = 0. Conservation of momentum means that momentum after decay has to be zero. Since you know the relative masses of the alpha particle and the recoiling product nucleus, you can estimate their relative velocities, and hence express the kinetic energy of either particle in terms of the properties of the other particle.
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    (Original post by Cora Lindsay)
    It is simple algebra. Assume the nucleus is stationary when it decays, i.e. linear momentum = 0. Conservation of momentum means that momentum after decay has to be zero. Since you know the relative masses of the alpha particle and the recoiling product nucleus, you can estimate their relative velocities, and hence express the kinetic energy of either particle in terms of the properties of the other particle.
    Thanks for your reply.

    I already understood this, I'm asking about the actual algebraic steps to do to get to the final form.
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    (Original post by Marc Fiorano)
    It seems like it's just a matter of some simple algebra but I'm having a complete brain fade atm.

    Any help would be much appreciated. Thanks
    \displaystyle \frac{Q_\alpha}{1+\frac{m_\alpha  }{m_d}}= \frac{\frac{1}{2}m_\alpha v_\alpha^2 + \frac{1}{2}m_d v_d^2}{1+\frac{m_\alpha}{m_d}} = \frac{m_d(m_\alpha v_\alpha^2 +m_d v_d^2)}{2(m_d +m_\alpha)}

    Does that help?
 
 
 
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