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Accelerating ions in E-field

  1. Jul 25, 2007 #1
    1. The problem statement, all variables and given/known data

    Assuming equal masses, how would the detection times of 3H+ and 3He+ compare [as they're both accelerated toward a detector in the direction of a constant E field]?

    A) 3H+ would have a longer flight time than 3He+.

    B) 3H+ would have a shorter flight time than 3He+.

    C) 3H+ would have the same flight time as 3He+.

    D) The radioactive 3H+ would always decay before detection.

    2. Relevant equations

    Now, I initially thought it was C: both would have the same flight time since they have equal masses and, therefore, equal velocities once PE (PE=QV) is completely converted to kinetic energy (v= sqrt(2KE/m)).

    But I realized-- in an 'aha!' moment-- that, although they have equal masses, they have UNequal charge, Q. The helium ion has 2 protons and 1 e-, while the H+ ion has 1 proton and no e-. If the Q of He+ and H+ are not equal, their initial PE = QV will not be equal, so their KE will not be equal. Because He+ has a higher Q due to 2 protons, the He+ has higher initial PE and greater KE after acceleration. It's flight time to reach detector should be less (ie faster travel) than H+, which has less KE.

    But C was the correct answer. Could someone point out where my reasoning is flawed? Apparently He+ and H+ have equal Q-values. Is this because they're both +1 cations? Does the ionic charge alone always tell us a particle's charge? As I understood, simply losing 1 e- (to form +1 cation) won't always equalize the charges between ions due to differential number of protons. The additional protons in He+ should account for a different (greater) overall Q compared to in H+-- no??

    I guess, in the end, I'm curious how you determine an ions Q. Is Q always going to equal the overall ionic charge-- or do we need to take the number of protons into account when we have ions with equal charges?

    Thanks a lot.

    3. The attempt at a solution
  2. jcsd
  3. Jul 26, 2007 #2


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    Science Advisor
    Homework Helper

    3H+ has two neutrons, one proton and no electrons. 3He+ has two protons, one neutron and one electron. The net charge of both is the same, +1. The masses are almost (but not exactly) equal - but you are told to assume they are. Hence, C. The '+' symbol is indicating total charge.
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