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An alpha particle and an antiproton are released from rest a great distance apart. They are oppositely charged so each accelerates toward the other. What are the speeds of the two particles when they are 2.5 nm apart?

alpha particle has a charge of +2e and is four times as massive as a proton

antiproton has a charge of -e but has the same mass as a proton

  • Physics -

    Because momentum is conserved, and total momentum is zero, the alpha particle will have 1/4 the velocity of the antiproton.

    Total energy remains zero. That means the two particles acquire kinetic energy equal to the potential energy LOSS, which is


    where e is the electron charge, k is the Coulomb constant and R is the final separation. The number "2" is there because the alpha has charge +2e, and the antiproton has charge -e. It is the product than matters.

    Set that equal to the final kinetic energy and solve for the velocity of either particle. The second particle will have to be expressed in terms of the first. For example,
    V(alpha) = (1/4)*V(antiproton)

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